You might try depressurizing your keg removing the post and poppet then putting a little crisco or vegetable oil around the poppet if you don't have any keg lub.
If you need to order or buy keg lub you might as well buy a poppet or two also.
Go light on the crisco it could cause you beer to have head retention problems.
Removing the tap from the other keg should not cause a problem unless it's leaking too.
Drunkensatyr suggestion also works sometimes to get a leaky poppet to seal be sure to remove the CO2 tank & depressurize first unless you want a beer shower.
Do what you like!
Brew what you like!