Does anyone know the hardware of a Nike+ SportWatch GPS?
The Nike website clearly shows that the firmware for the watch can be updated, so yes, in theory it is possible to change the program.  Whether you have enough information about the nature of the bootloader, the hardware environment, or the address space for any of the peripherals in order to do so, however, is doubtful.

Your best bet might be to try to get hold of a firmware update and try to disassemble/decompile it, and start from there. I've got no clue as to whether the firmware update file is encrypted or not.

Another option would be to see if all the info you need gets through to the host program, and if it does, just figure out what info is being passed and edit the host side.