Niiiiiice! 
 
Seriously, though, thanks everybody for their helpful advice. 
 
We've looked at snowballs's snowballs and they are definitely larger than Rufus's..... The sorting out of that might help. 
 
The kitty tranquilisers are a good idea, and might help the settling-in process. Wish we'd known about them earlier. 
 
I don't really want to rehome either cat. Snowballs is a couch cat, that keeps your lap warm, and if we had a guard dog he'd dig holes all over the place... so we have Rufus!