Q. As we are about to start the shofar blowing, a baal tokea that is a lefty, on which side of his mouth should he blow?
A. Rema (O.H. 585: 2) rules that it is better to blow with the right side. Mishna Berura (ibid. 7, quoting Magen Avraham) explains that it refers to the right side of the mouth, as the posuk teaches that Satan is on the right side. Shaar Hatzion (18) quotes a different reason, that since one wears tefilin on the left side, it is already protected. Sidur Yaavetz and Kaf Hachaim ( ibid.) add that the above also applies to the hand holding the shofar and not only the mouth.
Shaar Hatzion (ibid.) debates in regard to a left-handed individual, if the reason of blowing with the right side is due to the tefilin on the opposite side, then he may blow with his left side as he places his tefilin on the right hand. Then again, it may refer to the side most people don tefilin. Shar Hatzion, Beer Moshe, Kaf Hachaim (29) and others, seem to prefer this last opinion using preferable the right side of the majority.
However, most Poskim also agree that in need he may use the side he feels most comfortable with. so he may blow easier and better. (Piskei Teshuvos ibid. 5).
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a