For my admittedly larger chucks on my larger lathe, a hole was drilled into the chuck body. Into this is inserted a bar with a short matching piece of Silver Steel attached to it. With the belt tight, a swift blow on the end of the bar with a copper / hide mallet slackens the chuck.
To avoid risking the gear teeth, you could grip a piece of relatively large hexagon bar in the 3 jaw, ( Square for the 4 Jaw ) and apply a long spanner to the metal before using a copper / hide mallet on the outer end. The inertia of the motor and the Headstock usually provides enough resistance to a sudden blow, to slacken the chuck ..
If at first you don't succeed, give it another whack, and do follow through!
Remember the advice, not to run the chuck on under power. They will be quite tight enough, possibly more so, if just spun on by hand!
To reduce risk of chucks sticking, the threads and register on the Mandrel and in the chuck should be clean. Mine given a wipe, or brush, every time before fitting, (Ditto when changing from Internal to External chuck jaws. )
HTH
Howard