I mostly agree with the above. However, the formal dining areas have become incredibly casual, so while the "rules" still state that resort casual is the dress code, and that dressy attire is required for formal night, they do not turn anyone away, regardless of how casually they are dressed. Still and all, though, I find changing for dinner and partaking in formal nights to be one of the great pleasures of cruising. So check on how many formal nights you will have and plan accordingly.
Your shore excursions should determine what you wear, of course. If you choose to go caving or hiking, for example, you will need gear. But if you prefer to relax and hit the beach, a sundress and swimwear are fine. You can look into the possibilities before you leave for your cruise and decide if you want to snorkel, scuba, ride glass bottomed boats, kick back on the beach, go spelunking, hike or just rent a Jeep and go where you wish (a great option, especially on small places like Cozumel).
As for travel cups, we generally purchase drinks on deck, keep the cooler cups and are all set then to carry other beverages if we choose. They make great keepsakes and I find it easier than using space to pack them.
And go through your morning and evening beauty routines in your head and bring what you need. The on board "general store" is half to 2/3 alcohol and the rest is highway robbery if you need to buy an ibuprofen or a hair tie. So bring what you need and don't get robbed at the store!
Good luck to your DH! I hope you are able to take a cruise!