Funny story: my wife thought I was a little crazy at first, but I sold a car recently and got paid several thousand dollars in cash. I tried my best to check the bills myself and tried to make sure I could track down the buyer if I needed to then signed over the title and gave him the keys.
Best way to do this is do the transaction when the banks are open and have the buyer write a check and clear it at the bank that it was written on (with the buyer there). Clear it by converting it to cash at that bank. They will immediately check the account it is being drawn upon for sufficient funds.