Thats your choice. Our beliefs have consequences. If you really want Communion with Jesus, you will follow His ways.
We dont know what you need to confess, except what u told us. The advice is correct, to convalidate your marriage, while having remorse for abusing your priestly privileges.
It is our own priestly consecration which confers the Sacrament on each other.
Are you concerned because your wife is not Catholic??? Is she Christian? You can still seek a dispensation, i believe.
Edit: i just went back to your post again. Your wife “has no religion”. This is a tuff spot you are in. You cannot have a Sacrament marriage with a non-Christian. But i think there can be a dispensation still, somehow.
1 Corinthians 7
"Husband, how do you know you will save your wife?"