We have had problems with throttle cables. In the past we have been able to get away with cutting the cable - until it became too short - hence the problems.
You can use a motorcycle cable which is heavier and hopefully won't break or stretch as much. If the nub at the carborator end is too big, you can just file it down. We have done this and it worked just fine. Our moped does not have a nub at the top end..just a screw that presses against the cable to hold it in place.
Our problem has always been at the top end...until we cleaned out all the filings left from the old frayed cables. Probably another contributing factor to our throttle cable problem...live and learn.
Any "all purpose" motorcycle shop can help you if you can't get to a moped shop.
One question that I have is...how does one prevent the cable from fraying when you shorten them?