We like the Coconut Bay condos. It's a big house but not much more per night than the 7MB hotels and you can easily do shore dives right off the property. Dive Tech is just up the road and we didn't have crowded boats with them last trip even during high season. People also seem to recommend Turtle's Nest Inn and Christopher Columbus condos often, too.
There are lots of good dive ops on Grand Cayman, both large and small operations. Cayman University Divers is our favorite small op.
Coconut Bay Condos was mentioned and the Hepp's Reef dive site right off shore is really nice, but they are all 3 bedroom condos and that may be a bit big for your party?
Divetech offers one-bedroom units with onsite shore diving and boat diving packages at Lighthouse Point which is near CBC, see the link below, if they have availability I think that would be a nice option for you. It is north of 7MB on ironshore and you might want to rent a car, although cabs would work for you too.
Lighthouse Point Dive Resort in Grand Cayman
If you stay anywhere along Seven Mile Beach and West Bay, the dive shops will either pick you up on the beach or in a van and take you to the marina, so you can stay almost any where in that area and dive with whoever you want.
Are you planning to rent a car? Compass Pointe and Ocean Frontiers is a popular boat diving destination and the East End diving is excellent, but it is located about an hour from the airport (and from George Town and 7MB) so you should get a car if you stay there.
We usually get a car and stay in an apartment or condo away from 7MB like TNI, but we are there for a week and mostly do snorkeling and shore diving on Grand Cayman. If I were going for a short, dive-focused trip like you are planning - then I would look for something more convenient.
Sunset House Resort is on ironshore just south of George Town and they have an onsite dive op and shore diving. The resort is nice but not upscale and the shore diving is just okay, but if you are a photographer than you will like the Cathy Church photo shop and studio on site. The MyBar beach restaurants is one of our favorites.
Christopher Columbus Condos are gorgeous and there are other beautiful condo properties along 7MB (have you looked at VRBO?) but you want a short stay during the peak season at short notice - so you may have trouble finding availability - unless they get a cancellation.
I know that you said that you don't want a large resort, but if you can't find a condo then a resort like the Westin might be the best option for availability. Sunshine Suites condos are across the street from the Westin and you can pay a resort fee and have all the amenities of the Westin - and dive with whoever you wish in the West Bay area or with the onsite dive op Red Sail - they are a large dive op but they have big boats.
The Klimpton and the Ritz are very upscale and expensive resort properties, but most of the rooms at the Ritz are across the street and you have to use a bridge to get to the main hotel and the beach. There is a newly opened Margaritaville Resort that may have availability because it is new.
The Marriott and the Comfort Suites are also options, but that section of 7MB recently suffered serious beach erosion due to a tropical storm so not a good choice if you want a beach experience. The experts (and the optimists!) say that the sands will come back when the winds change - but I don't expect that they will be back by February. However they might have availability because of the beach situation.
I think you should start by looking at what's available for your dates. Not only is February the peak season, but the recent hurricanes across the Caribbean have made the islands that weren't hit, like the Caymans, even more popular.
