Dave,
I'd say better to err on the side of paranoia - and just don't take the chance of damaging the printing.
Instead, I'd probably take a nice soft piece of flannel or t-shirt and carefully wipe off the fingerprints and leave it at that.
Or, overcoat the thing with Future - you'll get a great shine and a very hard clearcoat and you can wipe off any further fingerprints without worrying about scratches.
Cheers
LeeTree