I looked around for quite a while on this one. Every source of information I could find said, "For your safety, diaper-age children must wear plastic pants or swim diapers..." If you feel that your daughter is not "diaper-age" any more, then you can skip the swim diaper.
While Disney leaves a lot up to the parent, as a fellow parent, I would just ask you consider that WDW is a new and challenging environment for some toddlers. They're tired, or they're preoccupied with having fun in a place they've never been, or spending all day in the water is a new experience, etc. And the child might forget some recently learned skills. If you think that won't apply to your daughter, then you can leave off the swim diaper. If you end up changing your mind, there are swim diapers for sale in the gift shops at the water parks and most of the resorts.
As for the snorkel question, I asked the same question myself right before my kids experienced Shark Reef at Typhoon Lagoon for the first time. The cast members at the snorkel station assured me that the equipment is sanitized between each use. They even showed me the process they use for cleaning the snorkels. You could also bring your own snorkel if you felt more comfortable with that. You can read about my related experience at Shark Reef
HERE.