Speaking of PTH, if it's not, if it's single side with unplated holes, you may well rip it out of the board, leads and all, obviously no bueno.
PTH is usually strong enough to pull leads out of the capacitor though.
Can do it with less stress by cutting the capacitor itself in half. Use an old pair of diagonal cutters that you won't mind denting (or causing accelerated rusting on). Cut it about at the waist. This should cut through the thickest part of the leads, which are upset or coined to retain them in the rubber seal, and below the roll of foil and electrolyte-soaked paper (or through it, which is okay too). Cut off the rubber plug (or melt/burn it off?) and clean up the leads as pigtails for your repair.
Tim