Rules question: Could you use Without My Hat to search for The One Ring (i.e., is "Immune to non-Master card effects" active even outside play)?
Other than that, there are some broken combos I can foresee with this; Three Golden Hairs, Phial of Galadriel, and several of the other boons are attachments, as is Banner of Elendil (you can play it with A Good Harvest).
In terms of non-broken uses, the main one I can think of is waiting to play this until you see what you need most. Need readying? Fetch Unexpected Courage. Need ? Fetch a Weapon. Need to brag that you bought the Revised Core Set? Fetch Valor. To me, though, 2 resources, even neutral ones, seems like a lot, leaving me thinking that, unless I plan to target something broken, I'll mostly go without Without My Hat.