Cellulose insulation can be an option if it's properly layered with styrofoam on both sides (like a sandwich) to create a waterproof barrier. Otherwise, the cellulose can retain moisture it is exposed to. On the inside of the cooler, add the rigid foam insulation before the plywood or FRP; this will help with both the moisture retention and with thermal bridging. There is loose pack cellulose and dense pack cellulose; loose pack is much more common. Take extra care to caulk or spray foam all corners and cracks.