Do you own either hat? If so, can you think of other items that one or the other hats displace? There's one main hat slot, and I would IMAGINE, both go there. The AFK does, so the OMFG probably does too. Since the Straw Hat fully encircles the head, I doubt that is it possible. Sorry.
Then again, look at all the things I managed to cram onto my head...
And why wear hats other than fish hats? I'm going to fish my a** off next month to get some, and maybe (hopefully, I'm REALLY gonna fish, A LOT) a trophy.