When I first purchased my ED30, it had finance on it.
The person I purchased from was a private luxury car dealer, and the ED30 was his 'runaround'.
Anyways, he gave me the following option:
1. He would give me the finance details, and I could pay it off myself, then give him the remaining cash to make up the full amount.
2. I could pay a deposit of £2k. He then clears the finance and I get proof of cleared finance when I picked up the car and paid the remainder.
3. I gave him full amount, and he cleared finance via the phone on the spot in front of me, We then wait for the finance company to fax across proof of no further interest in the car, which I would keep as evidence.
I decided to go for the 3rd option. I gave him a draft for the full amount. He then rang the finance company in front of me and cleared the full amount. He then passed the phone across to me and the person on the phone confirmed the finance had ben cleared. We then waited for the fax, which came through a few mins later to say that finance had been cleared etc. I checked this to confirm it had the proper company markings etc. I then rang back the finance company via their internet customer service number, just to double check it was them!
Once happy, i took the keys, the guy gave me a full invoice/receipt, and I left with a smile!
I would go with the same scenario if I were you. Inform the buyer you will clear finance on the spot with him present, so he knows its been done.