I’ve never traveled by plane,but I guess,in such case,the belt should be taken off before the flight and put back on right after...
Travelling alone would be a problem if the belt must be worn...Avoiding the plane,using train or bus(like Sara suggested),seems the best solution.
Going to the beach is really difficult,yes.Or we must wear clothes hiding it....Maybe using a pareo at the beach,taken it off right before going to the sea,and put it on right after?The belt would be visible with the swimsuir,but not for long,maybe short enough to not be noticed.