Don't do it.
I was educated on this issue as part of my training as a Confirmation teacher.
Technically, a parish cannot say "don't hold hands during the Our Father" because the present rules for the Liturgy do not specify what to do with your hands during the Our Father.
If your priest told you to hold hands he would be introducing extra-liturgical practices.
If your priest told you to NOT hold hands he would be introducing extra-liturgical practices.
In reality - those present at the CELEBRATION of the Mass do not become a unified community until AFTER they have received communion. Holding hands before receiving communion sort of short-circuits the celebration by showing a unified community BEFORE communion. If you want to hold hands with your spouse, that is fine, as you've been unified through the sacrament of marriage. But holding hands with strangers is the wrong symbolism.
During the Our Father I usually hold hands with my wife while saying the prayer, but never with anyone outside my family. Not even friends or acquaintances at Mass.
It’s another one of those things I guess. Some people are comfortable doing it one way, others are not.
I have no problem shaking hands with people I don’t know when it is time to make the sign of peace. But I don’t like all of the hand holding during the Our Father except with my wife.