Can Cetaphil-type products be used instead of soap? If so on private parts as well?

They have no rinse soap, it's hypoallergenic you do need to use water with it, but no need to rinse just dry off. They use it in the hospitals you can get it at drug mart and unlike wipes it won't irriate the skin.

I have heard there are adult wet wipes, similar to baby wipes, that can be used instead of soap and water that work pretty good.

Just Google "adult wet wipes" to see all the different types. Hopefully these will work for your Mom.

I think you mean "soap"? Get her MD to order a weekly bath aide who can show you how it is done, simply quickly and without chilling her.