Have you considered the spiritual significance of this dilemna? ?

Judges 3:15 But when the children of Israel cried unto the Lord, the Lord raised them up a deliverer, Ehud the son of Gera, a Benjamite, a man lefthanded: and by him the children of Israel sent a present unto Eglon the king of Moab.

16 But Ehud made him a dagger which had two edges, of a cubit length; and he did gird it under his raiment upon his right thigh.

17 And he brought the present unto Eglon king of Moab: and Eglon was a very fat man.

18 And when he had made an end to offer the present, he sent away the people that bare the present.

19 But he himself turned again from the quarries that were by Gilgal, and said, I have a secret errand unto thee, O king: who said, Keep silence. And all that stood by him went out from him.

20 And Ehud came unto him; and he was sitting in a summer parlour, which he had for himself alone. And Ehud said, I have a message from God unto thee. And he arose out of his seat.

21 And Ehud put forth his left hand, and took the dagger from his right thigh, and thrust it into his belly:

Slayed by the word of God literally.

Mat. 6:3 But when thou doest alms, let not thy left hand know what thy right hand doeth:

Made first flesh and then spirit.

I understand there is a spiritual meaning behind the left and right. Not sure if it is significant as to which hand one wears a watch.

The Spiritual significance is this: Discernment

As for the watch, it depends on your hand dominance as well as which side the pin is to change the time.

NO !!