Counteract joule-heating
thought about using a high frequency current to use the skin effec

Skin effect will make your current flow through less of the wire's cross-section, thereby increasing resistance, and thereby increasing heat – not only linearly, but quadratic. So, that's making things worse, quadratically with frequency. Don't do it.

That way, if I coated the structure in a heat resistant material, the current would run through that instead of the structure.

You need that coating to be of higher conductivity than the core wire. That's indeed done – tinned or copper-clad wire is a thing. If the coating was of lower conductivity, it would be worse than just making your wire thicker by the same amount.
But you'd still be better of without the skin effect – obviously, you still get lower overall resistance when you don't use high frequency. The current through the coating and through the wire will be split according to the first-semester-first-class-first-hour current divider formula, anyways.

So, I was wondering if it was possible to solve this problem at the root, as in not generating heat in the first place. If anyone knows how, please tell me

Use a superconducting material instead of your wire. No other options.
If you just want to reduce the amount of heat produced, thicker wires, or coating your wires with copper or silver and using the lowest frequency current possible will be the right solution.
Of course, avoiding to transport high currents through thin wires alltogether would be the best solution.