As a GTA modder, I should imagine this is the same for Bully.
Only replace CUTSCENE models with other CUTSCENE models, otherwise your game will crash or have a messed up cutscene.
Please note the following is an example.
If you don't want SP_NinjaR in cutscene, find the cutscene model of the character your playing as.
Say your playing as Johnny, find CS_GRlead_Johnny and replace all the CS_SP_NinjaR models.
Then when watching a cutscene wearing Red Ninja outfit, you'll be Johnny instead. Just with Jimmy's voice.