First, I had a weird lip on my cooler that made it so the top didn't actually come down to meet the sides. I decided to use a strip of faux leather to hide this after it was all covered in the paper. It actually worked pretty well, my only complaint is the fabric has enough stretch to conform to the shape of the lid so it got a little tight on the sides, but it looks great (you just have to be careful the cooler seals properly when you close it). The faux leather was just a scrap I had lying around from Halloween so it wasn't quite long enough and I had to use two pieces to wrap around the lid, if I had my preference I would have used one continuous piece.
Secondly, my cooler did not have handles, but it did have weird holes in the edges of the lid, go figure. I have no clue what these hole are for, maybe you can lock the cooler to keep out Fish and Game? (kidding) So, instead of wrapped handles I decided to put a braided cord on either end to make it easier to lift the lid (this is especially helpful because I covered the lip intended for use in raising the lid). Finally, my cooler had cup holders in the lid, this is the most obvious non-period detail about the whole thing and I will probably cover it with a cutting board most of the time... but I know we will want to use those cup holders so I didn't want to cover them permanently.
We will debut this bad boy at Boar's Hunt this weekend, with a little luck it will keep everything cold AND look good enough to pass peer scrutiny!