There are many dive operators here in Phuket and as others have said not all own and run their own boats, so you can end up on a boat with a large number of people. This is normally the case when you book with a dive center who do not have their own boats. Scuba Cat diving has its own boats and run all year around. We limit the number son board to 20 on the daytrips and we run a liveaboard with just 12 guests maximum.
We run daytrips each day and the liveaboard is doing overnight Phi Phi trips during the time your son is here. If you want more information just contact me and I will be happy to help.
Dive sites are mostly open for novice divers with a couple of exceptions and diving in the green season often give uncrowded sites. There is a mix of reef, wreck and wall sites available. If they wanted all sites then they would need to have the 30m license, but there are enough shallower ones to dive too.
Other things to do on the island are many, snorkeling, boat trips kayaking, waterfalls, temples, big Buddha etc, all can be booked in the resort.
They are based in Kata/ Karon which is included in all transfers etc.