Tiny GPS data loggers exist: I-GotU. I've not used one so I can't say how well it works.
I use one quite often, as a backup to record where I've been when I'm on rides where someone else is leading, and I would like to have a record of where I've been for later reference.
The IgotU has a significantly poorer accuracy than a decent handlebar mounted GPS, largely because it has a much smaller and possibly badly orientated antenna. It's probably perfectly adequate for this sort of purpose however.
Also, to get a decent runtime, you have to reduce the time between track points, but one point every 20 or 30 seconds will allow the battery to last 20+ hours, which is probably OK.
One of the downsides with it, is that it is hard to know if it's working reliably, I managed to have it configured wrong for the Bath Blast the other day, and it didn't record anything, but unlike a "conventional" GPS with a big display, the only difference between on and off is a blue LED which flashes every 15 seconds or so.
Having said all that, this sort of GPS is probably OK for this purpose, with the caveat that as with anything technological, things can go wrong in an non-obvious way (ie you delete the track instead of downloading it etc)