r,oril, we have the same boat (and I have AC powered LED Chrismas lights on also) so I thought I would pass on one more thing.
It regards the safety issue of using 110 VAC Christmas LED lights and the very unlikely risk of having the powered lights fall into the water with a swimmer near by. What would happen probably depends on salt content of the water, how close the swimmer is, etc - but it could be dangerous. And I would agree that the risks of this ever happening are extremely small (ie, don't let anyone swim near the boat when the lights are on).
Regardless, GFI outlets are a good way to protect for this problem. Pretty simple - just use a GFI AC socket coming off your inverter that power's the Christmas lights. Ie, take the AC out of the inverter and run it to a GFI socket. Plug the Christmas lights into the GFI socket.
The slightly tricky thing with this is making sure that the Green ground on the GFI outlet gets to the water. GFI only trips when some of the "hot" AC current flows to the green ground. If the light string falls in the water, it would trip the GFI only if the GFI ground is also in the water.
On the setup I just did, I used a "hardware store" inexpensive inverter to power the LED Christmas lights. On this particular inverter, the AC green ground is internally connected to the 12 volt DC ground. Since my DC ground is connected to the outboard, all I need to do for the safety issue is make sure my outboard is in the water.
A second small inverter I checked did NOT have the AC and DC grounds internally connected - so you should check this (just use an ohm meter between the grounds unpowered. In this case, you would have to make sure the GFI socket ground was somehow connected to the outboard.
As mentioned.. risk of any problem is probably extremely small - but thought Id post this just in case..