The buyer has to check the transaction. It depends a lot on how he does that. I would check a reputable blockchain explorer.
Let's say that the buyer checks in his own wallet.
If he has a full wallet, it may work, but that would mean the buyer comes with his laptop (why would he do that if all he needs for checking is a browser which he already have on the smartphone?)
If he has a SPV (Electrum, Mycelium), I think that there's a possibility he can have a corresponding (fake) server in his own network. But he will have to know what wallet to expect (to prepare the corresponding server), he will have to have his own custom DNS...
Overall I think that, although possible, it's not viable.
The seller has to know too much info about the buyer to have everything right. And quite some skills to get the buyer into that certain situation. And nowadays people just use the mobile data, there are far too many warnings to avoid using 3rd party WiFi.