With a digital, I would just take a ton of pictures - there will probably be some at least that don't have red-eye. It depends on the angle you shoot at, a direct shot will probably show the glare, but if the cat turns its head, there won't be so much for the flash to reflect from.

I use software (PhotoShop or Paint Shop Pro) to remove the red-eye from my cats' photos if the picture is good otherwise. That takes some practice to make it look realistic.