Good idea but is a federal crime to mutilate a bill. I prefer the way to have own paper money as paper wallets, just as casaciuos coins and bills, only with multisign addresses.
Yeah, the best solution would be to create an organization with reputable members who would provide their own public keys and print its own currency.
Caucassius coins could do it with its own coins and they wouldn't even need to hide a private key on their own coins, just coin them with a serial number.
The main point of my OP is to show that it can be done, as long as the paper currency is hard to counterfeit and that it has a serial number.