It's been a while since I saw the routine, but if memory serves these were the "standard" conical cups, taller than the Paul Fox design. Most dealers sell them. Johnny was a great entertainer. It's a good routine to learn.
Bill Palmer who posts here would be the best person to ask. His collection is on the Web and he can be contacted here email@example.com
(copy and past into your email) so you can get in and see it. The site is password protected.
You might also look at Jim Riser's site http://www.jamesriser.com/Cups/SelectingCups.html
He has an extensive collection and gives good advice on buying a set of cups. Jim knows his stuff.