Talk to the people at your local Fed Ex, and UPS delivery services about packing. They may have long " Bags" made of plastic that you can buy to cover the gun.
I would assume for the trip that the gun is going to get wet, or at least dunked. "Murphy" has a permanent seat in my back pocket, so I never expect better! :rotf: :grin: Put a good Grease( water pump, or any of the soft wax/vegetable oil formulas discussed here) in the barrel mortise before putting the barrel back in the stock, to protect the underside of the barrel from corrosion from the harsh Salt water, AND AIR. A liberal oiling of the metal parts of the gun before you take it on the ocean is also in order. Then take a bottle of alcohol with you to help you clean the gun thoroughly when you get to the island to be sure it will function properly.
If you can't find or make a thick gauged plastic case for the gun, then use several layers of plastic wrap to seal the gun, and use duct tape to close the package. Then put the package in a gun case, as it will shed a certain amount of water. There are silicon sprays available to treat fabrics and leather to " water proof" proof them. As long as the case is not held under water for too long, they tend to work pretty well. I would give any fabric lined gun case a coating or 3 of the spray, then test the case, by throwing a palm full of water on the case to see if the water beads and runs off.
The nature of the kayak is to cut through wave " chop", and only keep YOU dry because of the waist cover that seals the kayak and you from water. If you could find a kayak big enough to let you put something as long as your rifle INSIDE, it would be worth while doing so. But, Most kayaks are just NOT built with that kind of cargo in mind.
Don't hesitate to cover the muzzle, and the vent hole or nipple to protect the bore of the barrel. Oh, if you can find a gun case that will be long enough for your rifle, AND is designed to float, buy it. If not, don't hesitate to use an extra rope or strap to attach the gun to your Kayak, so that the rifle will not be lost to deep water, if you overturn. I am talking about a loop around the wrist, or even through the triggerguard that is attached to the boat, IN ADDITION to whatever keeper straps you use to tie the gun to the kayak.