It's probably rude and condescending to pat Shiro's lion form on the head or anything, but Waver's hand does briefly brush against the shoulder in a similar enough gesture to make it clear he's trying to say thank you.

I think that's a question worth figuring out. If you two aren't the only one to go through it, then that's something worth knowing and being able to anticipate.

Waver begins to follow in Shiro's wake, careful of where he steps just to be on the safe side.