I honestly don't think you have to worry about that bag disintegrating. It looks like it is in good shape. I wouldn't be afraid of dunking it. The bags that disintegrate are in really bad shape.
If you don't want to dunk, you can heat towels in the dryer and lightly stuff to reshape, then hang in in your bathroom for a few weeks. The moisture from your shower will help it reshape.
For the cut on the strap, I attempted to repair a similar cut by applying layers of leather cement. I then used a mixture of paint and Lexol to try to blend it in. It wasn't perfect (and was a pain to try to do), but it helped.
So jealous! I would dunk.
Thanks for the advice. I'll be dunking it this weekend!