I use superglue gel all the time for fragging.
Even better, if it's available at your local hobby shops or fish stores is IC Gel brand glue.
It is a special superglue formula that is a favorite of fraggers.
It comes in a large purple and white tube, and the reason it's a favorite is because the tip doesn't clog even after being used several times.
I had one tube that I used over and over again for months without clogging like regular tubes of superglue.
Also to answer your question about the coral being out of water,... corals in the wild are frequently out of the water and bake in the sun for hours everyday at low tide all over the world.
Here is an eye-opening video of an entire coral reef out of the water at low tide in Fiji:
YouTube - Corals at low tide Fiji
And here is a photo of part of the Great Barrier Reef at low tide:
As you can see there's a lot of misconceptions when it comes to corals.
Sometimes during a big frag job or demonstration a coral might sit out of water for up to a half hour before getting put back in the tank.
Of course, I try to work quickly and avoid leaving it out for too long, but sometimes it happens.
The only one I every lost in this way was a leather that accidentally got left out overnight.
It might have actually made it till morning, but it was sitting right where the A/C vent blows down so it dried out completely before I found it.
