You can use ANY weapon, but the incarnon weapons give the highest possible DPS bonuses, because their evolutions apply to Whipclaw (importantly the fourth evolution). [Magistar] Incarnon with Magus Aggress gives the highest average Slash DPS (i.e. much higher potential bleed per proc but 91% chance of slash proc per hit) while Mk-1 [Bo] Incarnon gives the highest consistent slash (230% chance of slash proc per hit but 5 times lower potential bleed proc size). Note, Magus Aggress currently does NOT consume charges on Whipclaw use.

The best incarnons are as follows, ordered by "Average Slash DPS"
1. [Magistar] Incarnon WITH Magus Aggress Arcane (+300% CD) with Edge of Justice (+100 dmg), Orokin Reach (+1.4 range), Critical Parallel (+16% cc/ +1 cd)
2. Mk-1 Bo and Bo Incarnon with Stalwart Oak (+90/110 dmg), Swordsman's Celerity (+20% movement speed), Absolute Dominion (+38% status chance).
3. [Magistar] Incarnon WITHOUT Magus Aggress
4. [Dual Ichor] Incarnon with Alchemist's Wrath (+90 dmg), Resolute Force (+7s combo duration), Absolute Valor (+34% status chance)
5. [Ceramic Dagger] with Breacher's Opportunity (+120 dmg), Orokin [Reach] (+1 range), Absolute Valor (+30% status chance)

NOTE, while Magistar + Magus Aggress gives the highest possible average slash DPS, Mk-1 [Bo] gives much more consistent slash procs per hit and is preferred overall for endurance.

If you DON'T have Arcane [Fury] on, use [Spoiled Strike] over [Buzz Kill].

Arcane
Melee Retaliation gives very little extra base damage especially if you use [Catalyzing Shields] (93 shield = 14% damage). If you don't run [Catalyzing Shields], at max shield of 465, we get 70% dmg, which is still pretty negligible in the grand scheme of things (just a bit better than [Steel Charge]). There is really nothing else better to use that affects Whipclaw however, so you should just run melee retaliation. Melee Exposure would cause corrosive to outweigh slash.

Preferred riven stats
Wanted Positives : Crit damage > Damage > Crit chance > Slash (can't be rolled on bo) > Combo Duration
Unwanted Positives : Elements, Puncture, Impact
Wanted Negatives: - Puncture, - Impact or any other harmless negative

If you have a riven with at least approximately 150% crit chance, replace [Sacrificial Steel].
If you have a riven with NO crit chance or < 100% cc, replace [Buzz Kill].