Attaching scripts to RootTemplates works as well! It's a bit different from adding treasure tables, I think.
A short description of what I did:
1) Created char script in my mod module with dependencies on Main and Shared; added it via Ressource Manager to my module.
2) Took the script ID and added an entry to the animals.lsb file (RootTemplates).
3) Copied the file into Data/Public/MyMod/RootTemplates/
Loaded my module in the editor and all rats - in that case - had the new script added.
But would be fine if it was easier.