The StandSecure works perfectly well in either hand — there's no separate left-handed or right-handed model. The only thing you choose at checkout is your size (Short or Standard).
For walking, simply use it in whichever hand feels most natural and gives you the best support. When you stand up, you use both hands — one on the top handle and one on the lower support handle — so which hand you favour doesn't matter. If you're ever unsure which side is best for you, your doctor or physiotherapist can advise.