A cat will not do that. It's not in its nature to do anything you want unless there's something in it for the cat provided the cat doesn't realise you will get something out of it as well, except for the occasional Siamese which may be too in-bred to realise what is going on. If the cat can escape it will; if it can't escape it will go to sleep, again except for a Siamese which will scream its head off. Try a dog or a hamster.

Moving on from animal training:

From the point of view of bending wood, bending 1/4 thick strips around a 50" diameter is a radius/thickness ratio of 100:1. I bent 3/16" pine around a 6.5" radius, 35:1, just made it with a pre-soak of 1/2 hour. WRC wouldn't do it reliably even at 1/8" thick soaked overnight, it probably won't make it at 100:1 either. This was kiln-dried wood, air-dried wood should do better.

You can steam or dry-heat wood, works best on air-dried wood especially hardwoods. Steaming weakens the wood allowing the grain to collapse on the inside of the bend where it's under compression, doesn't have much effect in tension, so the trick is to have something on the outside of the bend like a steel strip that will prevent it from expanding so it doesn't snap.

According to plywood bending data 1/4" Douglas fir 3 veneer or Okoume 5 veneer plywood will handle a 25" radius (there's that 100:1 again), sapele or meranti may not, at least with the outer grain running circumferentially. You can get 10-20% smaller radius by bending ply across the (outer) grain. Cheap ply will bend unevenly due to inner voids.

Terry