Shotguns are currently too few and diverse, while optimal mod setups are too inflexible to warrant having more than a single Generic build. So just go look at my Generic Viral+HM Shotgun build instead.

The last 2 mods flex depending on which build you want:
Corrosive+Heat: 6060/90Toxin+Blaze - For Ferrite Armor. Generally superior to Radiation as more enemies are weak to Corrosive.
Radiation: Blaze+6060/90Heat - For Alloy Armor.

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 = Tox/Ele/Heat > CC
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.
Riven replaces mods with similar stats. Just copy the build and insert your riven to compare the relative power of mods.