You should be able to look at the valve, to decide whether it is tubed or tubeless. Tubeless have a mushroom base to seal into the rim. Likely a small trailer might have a tube. Tubed tyres are easy to get off and tube can be repaired with a puncture outfit, maybe even a bicycle one.
With all of the hassle of tyre removal and tube repair, consider a new tube.
Unless it's relatively new, a new tube on both sides may be worth the effort
Yes, you can do it either way. A tubeless tyre might be difficult to remove from the rim, they tend to stick. A car jack placed between car and edge of tyre near the rim sometime works. Blowing the repaired tyre up, is much easier if it is a tube - it can be difficult to put the air in fast enough to a tubeless to get it to seal.
Get it repaired or replaced. Most tubeless tyres have ridges on the inside of the tyre which will rub and wear into the tube causing sudden deflation. Oh, and if it’s for a trailer, make sure it’s the correct weight rating. Is there a date code on the tyre?
Take it to a tyre place, they'll fix it or replace the tyre. I'm as tight as they come but its really not worth messing with tyres, especially if it's a proper commercial on a trailer.