Hey Peter
Yeah compositing is really your only solution if the geo can't blend shape to the new character.
Depending on what compositing software you have, you basically just need to perform a warp that simultaneously fades into the destination image.
There are some plugins such as
Re:Flex which can be used in After Effects, Shake and Fusion. It looks pretty cool, but the warp effect should give you what you need for a standard transition.
Just make sure to try and make the end/start frames in your 3D environment as close as possible to each other to reduce pain!
Good luck, let us know how you go.
cheers
Andrew