What is the OD of the pipe that goes through the cooler wall? You should be able to find an appropriate sized washer for the outside definitely, a fender washer works for most. It can tougher to find a foodsafe solution for the inside, i.e. stainless steel but it is possible. I found mine at lowes but I believe any well stocked hardware store or even an automotive parts store may have them.
If you have a washer on the outside and inside of the cooler wall it will solidify everything.
My setup has the following as an illustration. 3/8" Ball valve (Female on both sides) to 1.5 inch 3/8 pipe nipple two (or 3?) zinc plated fender washers through the cooler wall. Inside: the original plastic "washer" that was on the cooler drain followed by a stainless steel washer (which iirc is 1/2 ID?) then a threaded copper adapter tightened down on the pipe nipple leading to the manifold.
I helped a friend build a mlt and he had a 1/2" ball valve to work with already. We were still able to get appropriate washers for his too. Sorry, I cannot recall the details. May have done some adapters to different sizes...
Hope that helps some.