Viral+HM shotguns are pretty locked down when it comes to mods, the main flex option comes in the form of choice between Cold mods:
Primed Cold can be replaced with [Chilling Reload] for some convenience in the form of +Reload Speed, at the cost of lower DPS. Also saves a Forma if you care about that :D
As for 60/60Cold, it's pretty much always worse than Primed Cold (Chilling Grasp), even when you count the damage increase from the +SC through Viral.

Good Exilus mods:
Fatal/Galvanized Acceleration - The go-to for shotguns, because it improves range. Galvanized version is usually better, if you can fit it.
Vigilante Supplies - The only option that provides a tiny increase to your damage, while also bringing you extra ammo.
Soft Hands / Lock and Load - Nice utility.

Riven

Riven stat priority: CD > MS > Dmg = FR = Toxin > CC
Riven needs Dmg, FR or Toxin to replace one of those mods, if it has 2 of those stats it can replace 2 mods and open up a slot for Faction damage.
CC is pretty weak on Shotguns because of how low the numbers are; other weapon classes have a higher % CC bonus than CD, but for Shotguns they're the exact same, making CC a relatively weak Riven stat.