You should be okay using CA for the repair, but there are other considerations. First off do you have any pics to post? Some of my questions; is the elevator balsa? Are the elevator halves connected via a wooden dowel or other hardwood? Anyway a picture is worth a thousand words.

I have broken balsa elevators in half and successfully glued them back together W/O any problems.

Worse case take a the old elevator with you to the LHS pick out a replacement piece, take it home, recut the holes for the hinges put in place. The last thing if you decide to to the latter, two schools of thought for attachment are out there: place hinges where they need to go, and pin them with a wooden tooth pick to secure (drill into the hing where it attaches). The other is to CA the hinge in place, being careful not to get CA on the actual pined hinge section. Of course all this is if you even have pined hinges. Good luck I'll check back with you.

Steve