Ouch

, how thick is the fingerprint ? if it is only light and not central to the mirror you could ignore it for a while..
Pulling the whole spider vane assembly out by unscrewing the thumb or other screws on the OTA, then carefully washing the mirror with a solution without removing the mirror from the assembly will work, but then diag. mirror collimation will be needed on it. Then it gets a bit more complicated in relation to primary alignment. Are any of the forum members, or an austronomy club near you and could help ??