What methods can be used to cook Skipjack tuna other than frying it in oil?
A few suggestions:


Raw. If your fish is great quality and very fresh, and you have  a good sharp knife (just look up the way to cut it for the nicest texture)
Ceviche. This cooks (denatures) the fish with acid, rather than heat. Lots of recipes out there for great marinades, some with no added oil at all.
Seared. You only need to add rub enough oil into the surface of the fish to prevent it from sticking, to a hot griddle or flat pan.
Steamed. Often with aromatics. In a bowl to catch the juices, or wrapped in a loose but well-sealed package of foil or greaseproof paper (en papillote).


Gently poached in good oil is very nice, but I don't think that would meet your dietary requirements!

En papillote Is often done in quite a hot oven: the package enforces steaming inside; the fish isn't exposed to fierce heat.

All of these methods will be enhanced by your choice of recipe for dipping sauces, dressings, marinades,  sides, etc. There's no difficult technique in most of them. The lucky thing about good fish is.. the less you do to it, the better it is. (Almost). Look up the methods, and you'll find the recipes.

The only real danger is overcooking. You'll have to get to know your preferred doneness.