Hello again, Molly!
Saluting with the hand is a relatively new tradition in the Royal Navy, which was introduced under Queen Victoria. Prior to that the custom was to uncover the head.
Up until 1923 anyone who was unable to salute with their right hand could have done so with their left hand. However it was then recognised that the gesture was offensive to the people of India, which was part of the British Empire. (Indians traditionally use their left hand solely for cleaning themselves after using the toilet. It can give great offence in India to give or receive anything using your left hand). So saluting with the left hand is no longer permitted within the Royal Navy.
Since the use of the left hand to salute is now barred, it seems reasonable to assume that anyone who does not have the use of their right arm will simply come to (or remain at) attention while others salute.
Chris