Buy the key from the merchant.. but you'll miss out on some scenes where you are locked..

What do you mean recover? Once you get the key, you just un-equip the chastity cage. You should be able to use your cock then.  Are you still seeing the free-cock option greyed out? Btw are you also wearing the Armor of Anal Torment? I noticed wearing that prevent free cock as well. (If yes, decurse and remove that one as well)