You cannot use USB mice (or keyboards) in games. Only workbench. This means you need to have an Amiga mouse on standby.
You'd be much better off buying a (or if you are into DIY perhaps even making your own) PS/2 mouse adapter
which enables you to use optical PS/2 compatible mice with the standard Amiga mouse port. That way it will be 100% compatible.
Ok so £28 for a Cocolino at Amigakit is a lot of money... actually it is almost offensive so I'd consider making my own.