I wouldn't do the deal as I insist prospective purchaser sees the car and l would then need a deposit
on paper you have done a distance sale that might be difficult to prove otherwise
I had exactly the same a few weeks back, a prospective customer was asking daily for a car I had but I was waiting for log book for, she offered full money for it unseen and told me she now lived 100 miles away, I declined any money and indeed she never completed the purchase
I think she was trying to get a distance sale out of me by deceit
Sound familiar?