They could have fitted the whole ring / tape / mouse assembly into a small paper bag Aragorn could have kept it in his jacket and fed it little bits of lembas on the way how lovely x
Better yet, start the battle of pelannor fields as usual, cept you give that paper bag to Gwaihir and have him drop that shit on Mt doom like a gahdamn b52. NnnnnnnnnnnnnnnnnerrrroooooomKABOOM. Job done.