I have only the proper use of my right arm, and consequently have never used the double hauling technique. It hasn't prevented me from casting a line as far (and further) as the able bodied anglers I have fished with. It didn't stop me from getting into thr England Flyfishing Team and representing my Country at international level on three occassions, including the World Championships in 1986.
I suppose that what I am saying is that casting is really about timing as much as anything and unless you want to get into tournament stuff, using shooting heads and the like, going for extreme distance, who needs double hauling, which if done badly may impede your ability and would certainly give you tennis elbow.
Perfect your ordinary casting technique - you'll be able to cope without the rest.