Only TW2 has Skaven. If you have both games though it unlocks the Mortal Empires campaign in TW2 which is everything in a single campaign. TW1 has a chaos invasion main campaign in the old world and TW2 has a vortex campaign in the new world, with different empires in each. Mortal Empires is basically both at once with everything thrown in the mix.
TW1: Empire, Bretonnia (free DLC), Wood Elves(DLC), Chaos, Greenskins, Dwarfs, Vampire Counts, Norsica (DLC), Beastmen(DLC)
TW2: Slaven, High Elves, Dark Elves, Lizardmen, Vampire Coast (DLC), Tomb Kings(DLC)
They’ve also added a bunch of starting positions and legendary lords (faction leaders) either in paid DLC or for free. Also any DLC you don’t have still appears as AI characters, so Tomb Kings are still on the map you just can’t play as them.
But owning the lot unlocks the Mortal Empires mega campaign where all of that is playable at once.
EDIT: So specifically for Skaven just get TW2. If you have a particular faction of Skaven check the DLC as one adds Skyre and one adds Eshin, otherwise it’s stock Skaven and Pestilens.