You don't need to be motoring to snag pot warp. As stated before, in some areas toggles are used. They are particularly pesky when sailing cross current. Usually both ends of a string will have a pot. Lobstermen always lay in the same direction(else they cover somebody's gear in which case theirs will get destroyed). It isn't too difficult to determine the set lines. Full keel boats have the least to worry about. Sail drive..the most.
If you are transiting a locale with toggles, you best do it in daylight. Line cutters of all description will do little to help you if you draw the pot into your prop before the warp is cut. Your WILL stall out and you will fall off either down wind or current depending on which is stronger. Best tools to have: mask, snorkel and a telescopic pole that you can double water clamp a razor blade cutting knife to. Use the flat knives that have the extending blades that allow you to break off segments. Make sure you have both floatation ( short piece of a noodle float and wrist lanyard.
Some recreational lobstermen fish on the cheap. That means that don't use traditional pots and very often use low tide line. That means at high tide their gear is hidden and at mid-tide it's waiting for you just below the surface....