Noooo...You don't want to stay on the ship...That's my Birthday...You must celebrate...lol. We went to Key west on the Fascination for my birthday last year. Had never been there so we just took the tram into the city and walked for miles. Great photo opportunities. Visited Hemmingway's house. Saw chickens running around and signs protecting them. A mosaic car. Mile marker 1. We really enjoyed just strolling through the streets and seeing the beautiful houses and the plants are amazing!!!
I don't think I would bother with a ship's excursion, but definitely get off the ship and explore. Perhaps the best way to do that would be to take the Trolley Tour from the center of town. It offers hop on and off privileges at each of its stops, Whenever you are at a stop that you and the kids find of interest, hop off. When you are done exploring on your own, just return to the trolley stop and hop back on the next trolley as it comes around.
I've been to Key West many times when I had a friend living there. Definitely do the Duval Crawl - walk Duval Street (where all the shops are), definitely stop in at Sloppy Joe's, and most definitely do not miss sunset at Mallory Square if the ship is still in port (they also have crafts for sale by local artists). You can bargain with the store folks on Duval. You don't like a price? Walk out & they will come down on the price, if not, go to the next place & ask them to beat the previous price - they will do it! If time allows, also see Mile Marker 1. The Trolley ride is a nice (easy) way to see the town. There is alot more to Key West than just Duval Street! And don't leave without a slice of key lime pie!