|My DS had a similar bug only once (thankfully). I never did anything special with the diapers, just washed them on hot as usual. My thoughts were the same--not going in the mouth, etc. It doesn't seem to have been a problem, at least for us, and given the number of people on this forum whose kids must have had the nasties at some point, I don't recall having read much of anything about this, which makes me think that most people don't do a whole lot extra with those diapers.
If you want to do something, though, if you have a front-loader with a sanitary cycle, that might be ideal. Otherwise you could dump a pasta pan of boiling water in with your diapers if you have a top loader, so they will be washed with hotter-than-usual water. You probably could boil the diapers if you really want to, although that could pose problems for the snaps and/or the elastic. I do believe people have done it before without huge issues, though. If bleach would make you feel a lot, one round probably isn't the end of the world for your diapers; just make sure the bleach is diluted before you add the diapers.
There are always TTO and vinegar for mild disinfectant qualities, and the sun, as you noted.