4" is more appropriate, i dont think shrimp really bother live fish, you might want to consider a smaller shrimp, once in awhile a neocardina blue shrimp gets mixed in with a much of ghost shrimp, i'd say mine is 2" and all the fish leave him alone
im thinking but not sure, ghost shrimp would be easy pickings for a betta
check out petshrimp.com and view their's it'll give you some idea for the shrimp you want