As far as Belize goes, you'd be better off going with the cruise ship
booking.  It's a bit of a boat jaunt out to the dive site(s) and if there is
a breakdown, the ship will wait for you if it is their booking.  They'll
sail without you, if it is not.

I cruised with Royal Caribbean

Cayman was a rush dive thru Red Sails.  I did my own in Cozumel.  When
booking your own be careful between local time and ship time.

You will be using local dive operations anyway. The cruise ship
contracts with local ops, who come to the ship to pick you up. The
advantage of going with the contracted op is that if he's late, the ship
will wait for you; that's part of the deal. If you make your own
arrangements, you're on your own. Depending on who you deal with, an
operator you contract on your own might or might not pick you up and
drop you off at the ship, too. Price difference should be minimal.

gc