Seilerbird,
Here's how to both wash and dry your cat.
Thoroughly clean the toilet and then flush it several times. Add several ounces of shampoo to the toilet water and have both lids lifted.
Obtain and soothe the cat while you carry your friend toward the bathroom. It is important that the cat is purring comfortably. Then in one smooth, but swift, movement put the cat in the toilet and quickly slam down both lids. At first you may need to stand on the lid so the cat cannot escape. Do not get any part of your hands or fingers too close to the edge of the toilet lid because the cat's paws will be clawing out for any purchase that can be obtained.
The cat will self-agitate and make ample suds. Never mind the noises that come from the toilet, the cat is actually enjoying this. Next, flush the toilet 3 or 4 times. This provides a "Power Wash & Rinse" which has been found to be effective. It is not recommended to use the "Power Wash & Rinse" feature with small kittens.
Finally, have someone open the door to the outside and ensure that there are no people between the toilet and the outside door. Stand along side the toilet (not in the path between the toilet and the door) and quickly lift both lids. The now clean cat will rocket out of the toilet and run outside where the gentle flow of air passing over a fast moving animal will air dry the cat.