I custom painted a beak on my hwk, I tried to set it up to photograph and dropped it. The peg broke off inside he socket on the model and I can't remove. As far as I can tell there is no peg sticking out of the socket to grip with pliers. Is there anyway to suck the peg out?

You could try to use small (really small i mean ~2mm) drill to drill inside then apply some force to angle it to "lock" the drill inside and try to pull it out this way.

Other than that just glue the peg.