Don't know if they still make it, but I have a Sony GPS-CS1 that seems to be what you want. Runs on a single AA cell, has no display and attaches to a pack or whatever with a carabiner-style clip. When you turn it on there's a little LED that blinks to let you know when it acquires the satellites and then it just records the tracklog until you turn it off. Hooks up to a computer with a mini-USB cable to download the track data.