I have a parts bridle that has conchos on it that I"d like to take off for another use....and I can't get the darned things to budge! I don't know if someone used LocTite on them, or if they've just been on for a really long time...I've been using a grippy rubber cloth square to hold them still while trying to unscrew them on the other. Been trying to figure out how to maybe get some WD40 in the threads, but that is a conundrum too.
Are those the old time kind, with a rope border?
If so, you can put a cloth on the end of a flat screw driver, wedge it on the rope border and tap the screw driver with a hammer gently, until the concho starts turning.
Be sure to tap in the direction it will unscrew, clockwise, but some times you have to tap a bit both ways to get it started to come loose.
If you can get to the concho with a vice-grip or such plier, the concho protected with a cloth, you can get it tight around it and try that way.
Be careful not to use so much force you bend it.
If it has some kind of glue holding it, try a hair drier warming it up before you try to unscrew it.
I've had good luck getting stubborn conchos and chicago screws to give by folding the leather back (forming a U facing away from your screwdriver) and holding it tightly so that the leather presses against the edge of the concho.
It sometimes marks the leather, but it's never failed me.