(Just decided to make an Overframe account to save my current or planned builds)

So, the build itself (tested by another person, thanks to them (some videos from them at the end)):

Velox is a Status-based weapon, with a decent Slash bias (= its highest, innate, physical damage is Slash), which means we can do a Viral-Slash build (or you can use a pure Slash-status build with Crits and other +damage effects, if you have another way to give Viral to enemies...but that's not the point of this build, and [Velox]'s Crit stats are not the happiest ones either)

Note: Someone asked me to emphasize on one point: you need high status chance in a Status-based build because it increases the amount of statuses applied per time unit (for exemple: a second), but Status Chance itself has no impact on the element of the status(es) applied (it's something else, read the part about Frostbite/P.Pestilence/[Carnis Stinger] for the exact explanation)

Why Viral Slash ?
Viral status increases the damage dealt to Health, while Slash status deals some damage over time that is not affected by Armor (Armor being the main reason Steal Path and other endgame enemies have tanky HP bars)

• Lethal Torrent/[Galvanized Diffusion]: everybody love multishot on their guns...and for good reasons, it's really useful. I picked Galv. Diffusion over normal Diffusion because you want to kill with this build (if you don't want to, check another (better for that job) build/guide, and if you can't, I suppose there is a problem somewhere)

• Galvanized Shot: it's a source of status chance (great for a status-based build), plus it adds some heavy damage boosting once you put some statuses on the enemy (increased damage means your DoT status scales off bigger damage numbers, which means they themselves do more damage)... Sure you need to kill to get the +DMG effect going, but you should always find some fodder somewhere

• unranked Frostbite, unranked Pistol Perstilence, Carnis Stringer: the backbone of Viral/Slash builds. The Cold/Toxin mods allow you to add the viral damage type to your weapon (while adding less damage than the pure +Elemental mods, and while adding some extra status chance...both are great points btw), and the Carnis Stringer allows you to keep the Slash bias high enough while adding some good Status chance

Slash bias ? Why is low Viral damage good ?
First: you need to know that Viral status effectively caps at 10 stacks (having more is literally useless) and the damage against heavy units is from the Slash status' DoT.
Second: when your weapon applies a status, it rolls to determine the element of the status applied...and the higher the element contributes to the overall damage, the more likely to be picked as the status' element it gets

Imagine the game spins a pie wheel spinner, and each slice of the pie is every damage type your weapon can deal. The more damage you have of one type than the others, the more space it takes up on the pie wheel and the more likely that specific status effect activates.... So you don't want to have your Viral damage taking up half of the wheel, when you don't want to pick it more than 10 times, and you prefer picking Slash overall
And as a side note, unranked mods need less Capacity...which means less formas are spent to sqeeze everything in

• Primed Expel Grineer: Grineers are most likely going to be the tankiest and annoying-est enemies, so adding an extra layer of lethality specifically against them is not the dumbest idea... Do note that "Faction Mods" are accounted twice in the damage calculation of DoT status, which the main damage source is

Accounted twice ?
Anti-faction effects are applied to the original hit, increasing the damage dealt (that the DoT status' damage scales off)...and are applied to the damage instances from the DoT status (= when the target bleeds, it bleeds with extreme prejudice) afterwards, thus increasing even more the damage

• [Augur Seeker]: The mod is great for two reasons: it's an Augur mod (its set effect applies to the frame even if Aug.[Seeker] is the only Augur mod in the loadout, making shieldgating easier), and it benefits greatly the build's interests by keeping up statuses on targets, until said targets are cleansed by death

Shieldgating ?
If you take enough damage to deplete fully your Shields (unless it's Toxin damage or some scripted psychological damage, they straight up bypass shields), you get a weird scramble on your screen: it means your shieldgating activated, and basically you cheated death.
More seriously, when your shields breaks, you become temporarily invunerable (if you shields recharged fully since the last time you became shield-broken, the invulnerability period is longer btw), that's what "to shield gate" refers to

• [Primed Pistol Ammo Mutation] (really optional): I didn't find something that could really fit as an Exilus on [Velox], so...went with the default passive ammo recovery is great, there are no such things as "too many spare bullets"

• Arcane (really optional): If you REALLY want to invest a lot in [Velox], to the point of using an Arcane Adaptater...may as well choose the most fitting one ?

Merciless is a top pick because the Velox will self-sustain itself through its Slash DoT kills...just keep in mind the timer on the stacks

Cascadia Empowered could also be great because the [Velox] will quickly apply Statuses. A LOT of Statuses. And C. Empowered is really effective when you apply a lot of status within a small timeframe, and you deal low base damage (which is what is happening)

Dexterity can be worth if you use your melee a lot, but it goes a bit against what the build want (which is doing the killing itself...you'd build a "primer" (you use it to coat an enemy with Viral/other statuses so it ramp up Condition Overload/Galvanized Aptitude scaling buff) Velox differently)

Cascadia Accuracy/Cascadia Overcharge are not bad (or even great, considering we are talking about [Protea]'s sidearm), but would fit better inside an hybrid or Critical build (a build that take advantage of Critical stats, basically)

Deadeye is bad for the build because 1. Good Luck scoring lethal headshots 2. Kills from statuses do not trigger it...

But what if I don't have or like X mod ?

You have replacements, don't worry

• Primed Expel Grineer: the non-primed one works fine... that's like going from "overkill" to "less overkill"

• [Augur Seeker]: [Augur Pact] (+Damage) is good enough if you want to keep the Augur Set bonus, keep in mind it's additive to the +damage from the Arcane and [Galvanized Shot] (that means it's not optimal...but if you want to bruteforce lower levels until you get Aug. [Seeker], it works fine)
  Alternatively, if you already use Augur mods and you don't like the Status Duration, you can switch it out for Seeker (the Punchthrough mod...yeah, that's DE levels of confusion) so that works better against tight crowds

• [Primed Pistol Ammo Mutation]: Normal Ammo Mutation works fine for the passive ammo pickup effect...it was a "IDK" slot anyway
  You can try [Steady Hands] if the recoil is too strong to manage, [Trick Mag] if you want more shots but have no Ammo Mutation OR barely find ammo pickups, [Suppress] if you want to try silent [Velox] (you have better weapons for that imo, but as you want), etc
  Really, up to you on that one (and if you don't use it, that's one less forma to care about)

The recorded tests //from patch 31.1, so Eximi are way frailer on the videos than in-game now (Overguard mostly, yada, yada)

The build used in the recorded tests (the arcane can be different):

[Velox] Merciless Example

[Velox] Dexterity Example

[Velox] SP Incursion Example

[Velox] vs Acolyte (sad)