My interpretation is that the Barrow-Wights, while not necessarily aligned with Sauron, are dangerous spirits from the First Age. They are wicked enough to resist a restful death and powerful enough to be successful at it. If the reference that they are evil spirits sent by the Witch-King to inhabit the bones of fallen Dunedain or Edain is accurate, then they could still be brought into service of the Nazgul and by proxy Sauron, but that begs the question of why didn't Sauron make use of them in the making of his new army.
I prefer to think that they are unaligned spirits that have broken from Sauron's service and are motivated by a traditional undead hatred of all things living. By this measure I would interpret Gandalf's fear of one of the Barrow-Wights seizing the ring to be a similar terror that Galadriel had of her taking the Ring for herself and becoming a version of the Dark Lord with her own power corrupted to darkness but unbowed to Sauron. This same event taking place in the hands of a Wight would be orders of magnitude worse; First Age power amplified by the Ring and motivated by a spirit that not only wishes to dominate the free folk but destroy them completely. Enslaving the world is still less horrifying than consuming it completely.
Even if a Ring-wielding Wight was not the match of a Ring-less Sauron, the devastation that it would be able to bring about would very rapidly draw Sauron's attention, and "whispers of the Ring" would rapidly turn to "Oh, its right there" and the tearing asunder of Minas Tirith would immediately move to #2 on Sauron's to-do list.
I think no matter what, Gandalf is right; that would have been a Very Bad Day(tm).