The good quality canned foods you mention, should not produce a problem, at least not a prolonged bout of diarrhea. I would not be too surprised, though, if a cat on the diet you describe, had a bit of stomach problem in the shorter term, when you change foods -- just because, there has to be SOME way for the junk in his system to exit! (Sorry!)
It may help if you think about what diarrhea or mild episodes of stomach upset mean -- that the digestive tract is irritated. It's inflamed, or tender, or somehow, well, upset. Some things you can consider that can help that are soothing things like, herbal Marshmallow, or using Bach Rescue Remedy Flower Essence in his water, making the change in food in a calm, quiet manner. If the worst happens, and a cat gets diarrhea, confine him to an area where it's most easy to clean up the mess, and clean him off if you can without making him upset.
If your vet okays it, you can also fast a cat for a short period, to let its digestive system get a 'rest' -- so, if a cat decides NOT to eat anything for a day or so, unless there are other reasons why fasting is a bad thing, don't be too worried. This means your cat's digestion doesn't need to be working, so it can devote energy better to healing itself.
Offer a bit of unflavored Pedialyte (infant electrolyte replacer) if a cat has diarrhea, since that dehydrates the animal. Electrolytes help them to re-hydrate, faster.
In the long run, the Felidae is a much better diet so keep in mind why you're going through the short term misery together!!