Some people have had to stop suddenly because it was unavailable in their country. Most switched to similar medications but none seem to work quite as well. Mexiletine doesn't seem to be addictive, so it probably isn't harmful to stop cold turkey, but I would ask a doctor first if you do plan to quit.
I think the sudden contrast would make the myotonia seem much worse, but you would probably adapt over time and not notice the stiffness as much. I don't think it would actually improve, though, unless you modify your diet or are extra careful not to push against the stiffness. The more you tear the muscles, the worse the myotonia will get because pain also causes muscles to keep firing. Magnesium helps some people, and L-Taurine is a natural amino acid that has been proven to reduce myotonia.