This isn't really possible. You could try taking Military Control over the Vichy and Italian navies, but Military Control doesn't work properly for navies; the owning country AI can still move them and repeatedly will, screwing up all your orders. It can take months to get the Regia Marina over to the English Channel since they'll sail every way at once, and make up their own orders every day or two.
Perhaps, then, it would be a better idea to load as the Italian player and send their fleet to Germany as the expeditionary force? Of course, if you consider this cheating, you will find it unacceptable, but I don't see why not, since it would be equivalent to the proper behaviour of the units under Military Control.
BTW, is it possible to relinquish Military Control once you decide you've had enough?
Anyway, I think I once had a situation where the French fleet became the Vichy France one, but soon died fighting with the British Mediterranean task force. I was foolish enough not to take the Military Control and exploit this. At that time I was discovering that taking over the Suez and Gibraltar straits simultaneously effectively sealed the Mediterranean turning it into Mare Nostrum

, and was so thrilled with this idea that I failed to use the Vichy fleet in a proper way.

o