Thanks for all the input. it will probably take a few weeks for me to check things out. I don't know if there are spare cables around. (That leads other questions: is all audio
XLR cable shielded? Do some manufacturer's make better cables than others?)
The particular cable needs to be longer than what would appear necessary. The mic is mounted on a podium for the lector, but occasionally the priest takes this mic in hand if he steps down off the altar to talk to the congregation. The excess cable is coiled by the podium.
Regarding the mixer (or any of the sound equipment for that matter) - I don't know the make or model. Its back in the sacresty, which is of somewhat limited access. I'll see about checking that out.
Joe