I don't think much will change in a week, sites don't sell that fast, even the $50 ones.

You can consider using an escrow service for this transaction. The seller should push the domain to escrow (someone with Namecheap account) and you cannot use it until you pay the agreed amount.
I am quite convinced that the seller would also agree to a deal that will last a week (now only 2 or 3 more days).