I wouldn't say your wife's nor your name being on C&RT records would be proof of ownership of the boat but it might help . I expect formal documents are absent for many inland craft leaving little in the way of proof of ownership. Mind you most stuff we own we may not have retained proof and its not an issue in practice.
Presumably you have joint names on the boat insurance.
The reaction from C&RT is not unreasonable given you have, as far as they are concerned, added a new joint owner.
I think it may be just me who pays the extortion money/license fee as far as C&RT are concerned but I have other documents to prove my wife and I each own half shares in the boat.