change the target line on the shortcut to this,
c:\windows\system32\cmd.exe /C start /affinity 1 "C:\Program Files\Mozilla Firefox\firefox.exe"
the number 1 correlates to cpu 0 and if you changed it to 2 it would relate to cpu1 etc.
it should flash up a dos window and then close it as it launches firefox, not sure if it works on xp 32bit, but apperently its on xp 64 and vista and above.
lurkio, ive never tried it, just read about it. With the quote marks because of the space in the path you might need to remve the /C as it is possible that it thinks the end of the command is where the quote starts, shouldnt, but is possible.
Failing that method, there is somthing called imagecfg that Ive read about that can modify the .exe to always run on a specific core, but make a backup first as since it modifies the exe any patches etc will fail.