IMO, Hawaiian waters are much more difficult to swim in compared to, say, the Caribbean. Unlike Caribbean beaches, which tend to slope gradually, Hawaiian beaches tend to drop off quickly and deeply, which can translate into rocking waves, making entry AND exit difficult. I wouldn't let my child of any age snorkel, especially off shore, unless I was confident that he could tread water if separated from his floation device and, most importantly, not panic. Most people are naturally bouyant in ocean waters, except when they panic and start flailing. Learning how to flip over and float is a skill that everyone should master, right along with learning how to tread water.
I third the recommendation to go out on a boat for his first trip. Being able to sit on a ladder to put on fins and your mask is so much less intimdating than having to walk in backwards and time waves. Boats also avoid rip tides, plus all are staffed with lifeguards. If you can't do a boat tour, then certainly target protected bays that are recommended for beginners.
I recommend snorkeling vests for everyone, even great swimmers, for no other reason than because they make spotting you easier. They also come in handy in case of an unexpected cramp or rip tide, etc. However, you have to have the presence of mind to inflate it, which goes back to the "don't panic" mantra. I'd also recommend a wetsuit top, which adds warmth and added buoyancy. 7.5 year old kids tend to not have any body fat, and Hawaiian water can be cold even in the summer.
I see that you're looking into swim lessons. I think that's a great idea. BTW, private lessons are so worth it vs. group lessons, IMO. One on one attention makes a huge difference. And privates usually ends up being more cost effective than group lessons because they'll only need one or two hour lessons. As with everything, some instructors are better than others, so definitely get recommendations on teachers and work your schedule around the teacher instead of the other way around.
Good luck and happy snorkeling!