The person who took down the grid doesn't have to be the person who kidnapped Vegapunk, they could be separate parties.
Example: Shiryu is using his invisibility to scout the island. Thanks to Laffitte interrogating Koby with hypnosis, Shiryu knows the layout of the island. Shiryu turns off the laser grid to allow other BB Pirates (who he already cloaked) to sneak in.
Caribou wanders inside while the grid is down, then kidnaps Vegapunk.
Shiryu is the most likely option to me, though.
Pythagoras: "No! Our detectors aren't picking up anyone!" (notice how confused Stussy is, too? I really don't think she had anything to do with the grid)
"Dr. Vegapunk's main 'Stella' body has vanished."
To me, Oda is implying there's someone there who can't be seen. If that's the case...