I do a lot of dives on cruises, and from my experience, you should not have a problem getting to almost any dive op with a 0700 port time. Sometimes I use the ship's dive op, and other times use off ship vendors, depending on a lot of factors. However, I am not sure why you would discount diving with the ship's dive op at Cozumel. I dove six dives at Coz in March and May on three cruises using the ship's dive op, and had very nice dives on each cruise stop. Sand Dollar was the ship's dive op for RCCL and Carnival, and I had no complaints about the dive op, crew, boat, or dive profiles. Sand Dollar picked up the group at the pier then a 2 minute walk to the boat, followed a short ride boat ride north to their shop for gear rental and paperwork check. Drop off after the dives was a 2 minute walk back to the pier. NO TAXI REQUIRED. My shortest dive was 42 minutes and the longest 59 minutes. The shorter dive was caused by me having a minor problem with my own dive gear, but it did not affect the other divers' dive time. The dive op broke up the boat group into 4-6 divers per DM, somewhat grouped by experience, with each group splashing at a different time. I liked the fact that they did not terminate the dive when the first diver reached the briefed min air to surface. Instead, the DM shot a DSMB, and the diver(s) that needed to surface, did so and staying with the DSMB at the surface until picked up by the boat. The remaining divers continued their dive until the DM indicated it was time for all to surface.
Can the ship cancel an excursion on short notice? Yes, but the same thing can happen to off-ship vendors. If the ship is late getting to port for any number of reasons, will the off-ship vendor wait for you? Probably not, but the ship's op will adjust the dive time to accommodate ship arrival/departure times. It's a crap shoot in either case. The only real downside to using the ships' op is that you likely won't be going to the more southern sites like Palancar.