Distance selling regs. do apply, it’s absolutely this sort of situation they were created for. There’s absolutely no point in the expense of an independent mechanical check if its part of an Approved programme as the car will be warranted and will have been prepped to a decent standard.
What is a good idea is to get the dealer to photograph the car thoroughly and send you pics and also ask the salesman directly about the cosmetic condition of the car. When the car arrives, inspect it thoroughly and in good light, as you would if you were collecting in person. If there is anything that you weren’t made aware of get straight onto them and make the delivery driver aware of it.
Be realistic in your expectations though, a used car can never be made to look like a new one. Fine/small scratches and stone chips are a fact of life and although they can be touched in or polished, they can’t vanish.
Now for the controversial bit. It is absolutely in the dealers best interests that you are happy with your purchase. Despite what a lot of people will tell you, they are not out to fiddle you or sell ropey tat and so long as you make your expectations clear, they will do their best to fulfil them.
Good luck and happy shopping! 🙂