I was just looking around yesterday for a programmatic way to encrypt/decrypt a file with a USB fob. I used an Aladdin fob a while back for a similar project. The encryption was symmetric but the fob kept the key and it couldn't be exported - so it was safe enough for my application.
You could do OpenPGP encryption. It will generate a symmetric key, encrypt the data with it, and then encrypt the symmetric key for the yubikey's pubkey.
Is this Yubikey capable of something similar?