Is it permissible to have a condition in the nikah (nikkah) to skip mahr?

No, mahr can not be skipped.

Mahr is a pillar of marriage.

It must be given, and even if you say we won't give mahr, it will still be given and you'll still have to pay it as mahr al mithil.

As the mahr of the median amount that was given to women like her. So no, you cannot do that.