Keep in mind that, depending where and when you are embarking, you might have trouble finding a cab to take you to a store. If there are lots of ships embarking and debarking on the same day the cabs will be very busy. On our last cruise we were staying in Galveston the night after, so we waited to get off the ship so the "flyers and drivers" could get off first, and we still had trouble getting a cab. It took about 30 minutes.
Also, once you get on board, you'll probably not want to leave! Too much to do!
I bring some drinks (2 six packs of Diet Coke) and some snacks in a small carry-on along with my regular carry-on luggage. Then I use the small carry-on for all those things I MUST buy on the cruise!
So, I guess, to make a long story short (too late!) I think you should just take your drinks with you.
Have a wonderful cruise,