Jon answered it in Season 7 Episode 5, when they were planning the Wight expedition and someone questioned feasibility of the plan:
The first wight I ever saw was brought into Castle Black from beyond
So from that precedence, he was certain they could do it again. The first wight mentioned here are the ones Jeor Mormont brought in Season 1.
This is inconsistent however. Show adapted book scenes for Season 1 but in Season 7 they are making their own story. Doubt it will happen that way in the books.
Anyways, a speculation can be, as long as a Night's Watch man accompanies a Wight, it can cross. But then the question is, Why did Benjen think he couldn't cross with Sam?
The spells on the Wall seem to be tied to spells on Three Eyed Raven's cave as pointed out by Edlothiad, so it is possible that Bran rendered them useless. But then again, Wights did cross the Wall in Season 1, Long before Night's King touched Bran.
Also they had a ship, so they could load the Wight on the ship and circumvent the Wall.
As it happened however, they had air-support when Dany answered Jon's call. But Jon didn't know she would come when he was planning so it could not have impacted his planning.