Can a non-Catholic minister be involved in a Catholic wedding?

Yes, but he will first need to obtain permission from the bishop. The norms for active participation by the non-Catholic minister during the liturgical celebration are as follows:

The local ordinary can permit the celebration of mixed marriages during Mass either in individual cases or in general at the discretion of the pastor. A non-Catholic priest or minister may be present and actively participate in a Catholic liturgical celebration of marriage. He or she may be invited to give additional prayers, blessings, or words of greeting or exhortation. If the marriage is not part of a Mass, the minister may also be invited to read a lesson and/or to preach. However, only the Catholic minister may validly ask for and receive the consent of the parties in the name of the Church. (New Commentary on the Code of Canon Law, 1348)