Not sure about the SCUBA question. We always use Eagle Ray Divers in Cozumel. Here's a link to their website.
http://www.eagleraydivers.com/
As for shopping, it depends on where you come in to Cozumel. Hurricaine Wilma wiped out all three cruise piers. Some ships tender in and some can dock.
The Punta Langosta pier is newly rebuilt, can dock two ships and is right downtown. You can walk it or there are little "bicycle taxis" built for two. No charge for that, just what you want to tip. That is the closest to shopping.
International Pier was partially rebuilt last time we were there back in March. International Pier is about a five minute cab ride (about $5) from town.
Puerta Maya was still under construction on our last trip, don't know if it is open yet but I don't think so. When we were last there the tenders were delivering passengers to Puerta Maya but the shopping area was still non existant.
Perhaps someone who has been there recently will have more imput.
=funsign on your cruise