We actually ended up doing it and having a blast! We just booked directly through Graycliffs and that is ABSOLUTELY the way to do it. Graycliffs is a very easy, quick walk from the dock so we really couldn't justify going through Royal Caribbean. They basically bring you out a bunch of types of wines to first sample each of them then you can start mixing away. Once you have your perfect mix you then bottle and cork it so you shouldn't have a problem on a flight. After we bottled we even had enough left over of our mix we had enough left over to have another glass of wine. Not gonna lie we after all of the tasting we may have wandered the streets of Nassau pretty buzzed. They are very generous with their wine lol. We ended up having to check our bottles at the dock with Royal Caribbean but got them back on the last day of the cruise. Graycliffs also saves your mix if you ever go back or want to order more to ship home. We would definitely do this again.
P.S. I will also say we are not wine snobs but everything tasted good to us. The previous user is correct that they don't grow the grapes on the island, they are shipped in (our batch from Italy).