As newbie divers, I am guessing you do not own your own gear. For that reason alone, go with the cruise ship dive arrangements! You will need to meet the boat, go to their facility and get fitted for all gear, then go do the 2 dives, return to facility to return gear, then back to cruise ship. This will take the majority of the day.
If you book with a dive op on your own, they will have to do the same... take you to their dive facility to fit you for gear, then go out to dive. This means they cannot put you on a boat already scheduled to go out as those people will have their gear already.
So ... unless you are booking at least 4 people for the boat to make it cost effective for them, you may have issues finding a dive op that wants to book with you. Cozumel has SMALL dive ops primarily, with only 1 boat each that seats 6-10 people. They are not going to hold up their boat for morning dives just to fit you for gear. I know you don't want to hear this, but most land-based divers in Cozumel do not want to dive with people from a cruise ship for this reason.
Go with the dive op arrangements through the cruise ship. It will be a more pleasant experience for YOU, as a NEW DIVER. Once you buy all your own gear and get more experience, then I would recommend you book on your own, but not until.
Just my 2 cents.
robin