By Big Folk, did Aragorn mean Elves and Dwarves? If not, then the Dwarves could still traverse the Shire in order to continue trade. Also, those border Hobbits with a bit of greed could offer to transport goods across the Shire for the Big Folk for a bit of coin.
On the other hand, after a few centuries when the big bad folk eventually decide that they are hungry enough to start eating those fat little Hobbits (never seen but spoke of in tales of lore), they might break the ban to find that no Hobbits exist, just a bunch of somewhat shorter people who obviously got there first. Hmmm...
Or Eru could step in again like when the Big Folk violated that other Ban...