"Referrals" are very common. Up where I live, many people do the classroom and pool part of certification here in the winter and then go down to the caribbean to do the 4 open water dives/checkouts dives. This is how I got certified. Not sure of why you're wondering about pool versus shore dives, but one of my considerations when choosing a dive shop in Cozumel to finish my certification was shore versus boat dives. At some shops, all 4 open water dives are conducted from the shore, at others, the first 2 dives are done from the shore and the second 2 dives are done from a boat on a reef. It may cost a little more to finish the referral if 2 of the dives are done from a boat versus the shore, but to me it was worth it. It's possible that some shops do all 4 of your open water checkout dives from a boat, particularly if you've done the classroom and pool with them.
Even if the "pool" dives are conducted in the ocean it won't be unmanageable, if you're having any concerns like that. Or, maybe you're hoping the pool dives are done from the shore instead of the pool. In that case, just inquire with the Cozumel dive shops you talk to. In any case, I think it's pretty common to mix the classroom and pool dives, meaning that you won't be in a classroom for 2 days, and then move to the pool to do that stuff. It's generally "a little classroom, a little "pool" time, a little classroom, a little "pool" time".
Don't know how long you're going to be in Cancun, or what your other considerations are, but if I needed/wanted to split up the training, I'd do all 4 of the open water checkout dives in Cozumel.