I went to this cabin in August of 2011. There is no trail into the cabin so the privacy should be good. The Wildlife Refuge area has a done a great job fixing up historic cabins and this is a great example. It looks a little rough on the outside but is very nice on the inside. The plane is shown in front of the cabin but there is a good place to tie up in the stream 100 feet away which is very protected. The lake is a little small so if your plane is a little heavy check out the lake size. The cabin is good for two but not a crowd.
Link to Kenai Wildlife Refuge Area http://www.fws.gov/uploadedFiles/Region_7/NWRS/Zone_2/Kenai/PDF/cab_Trapper_Joe.pdf
This cabin does not require a reservation, show up and it is yours.