Fritz,
Try clamping the feather between the two halves of the jig with a spring clamp and hold onto the clamp.
If you aim the nozzle away from you and pass the edge of the jig over the very edge of the nozzle, it will burn the feather just fine without setting yourself on fire. It doesn't take much heat to burn off the feather.
Kyle, that's real funny. I'm gonna call those my brokeback fletchings from now on.