I believe the sword and the salute have something in common.
If you are saluting with your right hand, the sword is not in that hand.
The whole issue is directly related to RIGHT and WRONG. Rather than right and left. Right is a moral absolute a foundation based on God given rules for, (wait for it), not radicals, but happiness, joy, salvation, peace, etc.
I have saluted with my sword in my right hand many times. you merely bring it up close to your chin inclined slightly away (~45*) to demonstrate your respect (hold for the return of course). ;)