Zap-a-Gap is one of many brands of medium-thickness CA. I prefer Gorilla's Superglue (also CA). It's about the same thickness as ZaG and it's used exactly the same way.
The advantage is that it contains rubber so it's less brittle and more resistant to shock. And it doesn't have that strong CA smell. And, IMO, it has a better cap.
Yes, you will need an accelerator. Thick CA dries much more slowly than the thin stuff.
(Gorilla's Superglue should NOT be confused with Gorilla Glue. It's completely different stuff.)