I did this in my shop, where I had 4 double overhead florescent fixtures. Here's what I learned:
First, they DO make drop-in LED tubes which will still work with the ballast. But I didn't go that route. It's harder to find direct-connect LED tubes, but there are several advantages. First, the ballast will eventually die someday, why set yourself up for a future re-wire? Second (and most important on a boat) is why would you want to power up a ballast? The whole point is to save electricity and increase longevity.
That said, there are two types of direct connect (at least on the full-sized tubes.) One has power on just one side (one "tombstone") while the other has power on both ends of the tube. You need to know which kind you bought when you re-wire.
It's a very simple wiring job. Good beginner project if you're so inclined.