So if the threads are a 1/2" NPT, I measured some fittings around the threads with a digital caliper and got about 0.81-0.83". A 7/8" hole would accept those, I think that's the usual suggestion. Hex nuts for 1/2" NPT sometimes have an o-ring channel and that's why I mentioned the o-ring. But a flat (not necessarily thin) rubber washer works too, I have some fittings with those too. The inner diameter there would need to be about 7/8" and the outer bigger than your drilled hole. As far as a metal washer, I find sometimes on the outside these help to stabilize the fitting. I have three vessels, all keggles, with multiple ports and sometimes different types of washers (rubber and SS) and o-rings. You might have some flexibility in the walls of the cooler that affects things. Perhaps a wider (Outer diameter -inner diameter) washer helps there to spread out the force. Thinner (like paper) will conform more to the curvature of the cooler.
But having an extra washer is always a good idea in case you drop it, put it down where you can't find it, need it later. I bought a box of o-rings either off Amazon or from harbor freight which has a bunch of different o-rings. Those are numbered though.