Add the required amount of shampoo to the toilet water, and have both lids lifted.
Obtain the cat and soothe him while you carry him towards the bathroom.
In one smooth movement, put the cat in the toilet and close both lids (you may need to stand on the lid so that he cannot escape).
Do not get any part of your body too close to the edge, as his paws will be reaching out for any living flesh they can find. The cat will self-agitate and make ample suds. Never mind the noises that come from your toilet, the cat is actually enjoying this.
Flush the toilet three or four times. This provides a "power-wash" and "rinse" which I have found to be quite effective.
Have someone open the door to the outside and ensure that there are no people between the toilet and the outside door.
Stand behind the toilet as far as you can, and quickly lift both lids.
The now-clean cat will rocket out of the toilet, and run outside where he will dry himself.