Here's a better choice: Stay put. If there is no good drop option, hit your ball off the path. Cart paths typically provide flat lies, often paired with an opening back to the fairway or toward the green. Using any club from a fairway metal on down, you can make the sparks fly without hurting yourself or ruining the club.
Set up with most of your weight on your front leg to promote a steep angle of attack that will add loft. Don't try to pick the ball off the path—make sure the club bottoms out. If you play this shot with any high-lofted iron, you'll get pool-table backspin like you see on TV. Steel wool can remove any scuff marks on the soles of your clubs.
You can fly free of dastardly divots with the same technique you would use to escape from horrific hardpan in the rough. The key to both shots is making sure that the clubface hits the ball before it makes contact with the ground. If you're in a divot, it's also vital to check your alignment. Make sure you're aiming where you want the ball to go, which may not be the same way the divot is pointing.
Set up with your weight on your front leg, as with the cart-path shot, to promote a steep angle of attack. Position the ball toward the back of your stance and choke down about an inch on the club—that will help ensure that you strike the ball first. Take care not to tense your forearms, wrists, hands or shoulders in anticipation of impact, because tension can throw the club off path and lead to skulled or chunked shots. Now you're ready to relax and swing away—this trouble shot is simpler than it looks.
HANG TOUGH: ESCAPES FROM UNEVEN LIES
When your ball is in a hanging lie on a slope above your feet, the tendency is to curve the ball left of your target. Try visualizing the ball rolling across the slope you're playing from. That will help you gauge the curvature and decide how far right of the target you should aim to accommodate it. Because the ball is closer to you than normal and your swing will be flatter, use a more-lofted club and choke down.
If the ball is below your feet, you'll tend to push or slice the shot to the right. Allow for the lie and for this left-to-right curvature by aiming to the left, using a longer club than usual and gripping the club at its full length. Now swing normally and let the ball—and your troubles—fade away.