Tanning takes time, which means you prepare the skin with fat, let the tanning act for a time (duration dependent on the size of the skin), with the skin lying on the ground. Now, if you tried that on a water craft, I wouldn't be surprised if the skin remained where placed in the geography, i.e. on the water, rather than on the craft, so you might want to return to that location to look for the skin (I'm not saying it will be there, only that it would be a logical place to look for it).
If you tried to do the same thing while cooking, the game should "fail" the cooking of the meal, as you're removing the pot from the heat source when you move the craft (unless the pot is left floating on the water).