There is no RULE requiring the right hand!
http://www.ewtn.com/library/liturgy/zlitur375.htm
ROME, 6 SEPT. 2011 (ZENIT)
Answered by Legionary of Christ Father Edward McNamara, professor of liturgy at the Regina Apostolorum university.
And yet,
there is no deep theological reason for preferring one hand or another. It is a question of practicality and longstanding custom, similar to the different ways of making the sign of the cross, moving the hand from right to left among most Eastern Catholics while the Latin rite traditionally prefers a left-to-right movement.
It is true that there are many biblical passages that speak of the power of God's right hand, and of Our Lord sitting "at the right hand of the Father." The literary figures contained in these texts are significant in many theological contexts and are certainly related to the liturgy's general preference for the use of the right hand. But I think
it would be forcing the issue to use them to exclude other possibilities, or convert the use of the right hand into an absolute rule. These texts simply reflect the use of universal symbols of power grounded on the fact that 90 percent of people are right-handed.
If circumstances warrant it, then an alternative mode can be adopted. For example,
when Blessed John Paul II broke his arm he felt no qualms in using his left hand to impart the apostolic blessing. Likewise, a person who is unsteady on his legs could genuflect according to whichever member gave greater balance.