Maniac was, indeed, quite crazy -- if you'll recall, Operation Thor's Hammer took its toll on his psyche. He survived the destruction of the Tiger's Claw because he was in the psych ward on the Austin at the time.
We know for certain that Iceman, Angel, Spirit, Blair (and a few others who are unnamed) specifically survived their patrols that day... by the time of Jazz' comments, of course, Iceman has since died at B'Shriss. (Of course, Carl LaFong, if he's a different person, also survived
).
Paladin survived because he had "retired" and gone off on another secret assignment.
Hunter survived because he was still on furlough (in 'Freedom Flight').
Doomsday and Jazz (well, duh) survived because they'd been assigned back to the Austin.
Why Hawk survived is a bit of a mystery... he *was* back from OCS, but he may have been assigned to the *Austin* rather than the Tiger's Claw -- or he may simply have been on patrol and survived.
Various background characters survived for odd reasons, too... for instance, a pilot named Vanderman in Fleet Action is a Tiger's Claw veteran -- he'd been shot down and presumed dead, but in actuality survived on a Kilrathi held planet until later being found.
We don't know how Shotglass survived -- presumably he simply wasn't on the 'Claw. (Given that he was the same age as Paladin, it might be reasonable to assume he retired around the same time...).
Halcyon *was* to be promoted and sent back to HQ -- but he hadn't yet been. He was killed.