I think Richard has a good idea. If you can get the release off, it might take enough glue with it to get things working again. The heat isn't likely to liquify the glue, so there is little worry of getting the glue farther into the camera.
Once the release is off you can remove any remaining glue on it with some warm water and perhaps a tiny brush.
For the camera, it's probably a simple repair, but you wouldn't want water in the release while it's on the camera. Taking the top plate off probably isn't difficult, but if you aren't comfortable with the screw turning, it would be best to send it in, as you've noted.