Would this work?  Set up a service wherein people create accounts and deposit BTC, like a bank.  They submit two things to the service.  A PIN of their choosing and a scan of their fingerprint.

Merchants have a register and a fingerprint scanner than can access the bank.  If sale price is 1BTC, you simply key in your PIN (so the service doesn't need to search all fingerprints in the database, only those with that same PIN) and scan your fingerprint.  When the system matches the fingerprint to the PIN, they send the BTC to the merchant.  Now you have a transaction with no cash and no card.  Only a number in the buyer's head and a finger on his hand.

The problem with this is that a fingerprint is not a private key, so this approach requires the private key be stored on some server somewhere.

A better approach is to store your private key on a smartphone.  Put a QR code sticker on customer side of the cash register (with the cash register's Bitcoin address) and scan it with your smartphone, enter the amount, and the phone sends the payment to the cash register.  Alternately you can have display on your side of the register showing a QR code with the address and amount, so you don't have to enter it.

For protection against loss or theft of the phone, you can have another copy of the private key somewhere.  If necessary, you use that other copy to transfer your BTC a new key, hopefully before someone finds and cracks your phone

Unfortunately Bitcoin doesn't really do "instant" payments, so there are some issues with this.  Search on the forum for "vending machine problem."

I work in the banking industry and get fingerprinted regularly.  Might as well skip the fingerprint part, which would leave just a PIN protecting the bitcoins.