I used to put Kockas carrier on top of one of those 4 wheeled shopping trollies, it fit snuggly in the top. We went on train to vets like that and she was a nosey devil watching everyone and everything. She didnt like it unleass she could see out of the train window, only one stop.
However it meant she didnt get swung about in carrier ands of course you could cover it with a towel if William gets very upset.
Both William and his friend are lovely