Well, the right cone was easily drawn, but the left, not so much. Letting it soak in penetrant. Will apply just a bit of heat. Very small square shank on these little fellas and not a lot of purchase.
By "cone" I assume you meant nipple....the question now is will a new one screw in and tighten up ? If not you'll need a gunsmith versed in muzzle-loaders to tap to a bigger size nipple.
Another thing to look for after you get the nipples out is if the seat is corroded away...the nipple hole wasn't a straight shot through the breach plugs. (With all the visible corrosion I suspect the seats will be corroded if not gone entirely).
Another thing that scared me about this gun is the fact that some amateur tried to remove the breech plugs. The barrels have to be "supported" to remove the breech plugs or damage to the ribs/barrels most likely occurred.
(Most heating and air supply houses around here have Kroil).