If you have resoldered the electrical connections and are sure the pots are still not functioning or "Noisy" and are destined for the e-trash, the safest way to remove without damaging the main board is to cut the the solder lugs one by one with a small wire cutter. Remove the complete pot mechanism—note: the values normally printed on the pot.

The plated through holes for the component ALL need to be cleared of solder to enable the new component to be uniformly fitted through the holes

Plated through holes(PTH) can be de soldered with a hand held vacuum de solder tool or copper braided wick

Do the hard work now so you can just "plug and play" the new components when they arrive