You can give the vendor the private key you used to create the pubkey with. If you are using electrum, click the addresses tab, right click on the bitcoin address you used to generate the pubkey and click "Private Key". In bitcoin-qt, go into help, command console, and type "getprivkey xxxxxx" where xxxx is the bitcoin address you used. Get the private key to your vendor via any channel you can, 3m4il or b1tm3ssage.