Chris wondered:

In a word... no.  Traditional cruise ships don't allow partial trips.  You'd
have to purchase 2 separate trips, one to get there, one to get home, and even
then it'd be iffy whether they'd allow boarding in Cozumel (usually only done
if someone "misses" a previous embarkation or port).

However, I seem to remember a ferry service from Florida (Tampa?) which might
fit the bill for you quite nicely.

Amber

This is what has been referred to as an 'extended port tour'.  A pax
books a cruise package, with an extended stay in one or more ports
along the way, completing the cruise on a deferred date.  About a year
or so ago, I was contacted by more than one cruise company about
booking some foreign property I own for extended periods (and reduced
price), ostensibly for this very reason.  As I recall, a couple of
hotel owners in my same are were also contacted.  One: I never do
business with cruise lines.  Two: My property managers don't need
anyone's help keeping my places booked outside the blackout periods.

Apparently, their marketing departments never put enough together for
it to work - although I can see the benefits if a market could be
developed.