I don't think the seatbelts in a shopping cart would help hold a guinea pig at all. And I'd be afraid to put them in the child seat because the leg hole is big enough for even Fuzzy to fall through. But it would be fun to bring the pigs out with us to the store. Or anywhere else for that matter.
They would probably freak out at all the people, though. I think the most they've seen at once is eight.