Can a male Catholic and a female Non Catholic have their marriage blessed at the Sacristy?

Cathy Caridi, JCL, is a canon lawyer who has a blog, and she commented on a very similar situation to yours. Let me try to paraphrase what she has written about it:

According to Canon 1108, a valid marriage where at least one of the parties is a Catholic must be officiated by the local Ordinary, parish priest, or a priest or deacon appointed by them:

1108

§1. Only those marriages are valid which are contracted before the local ordinary, pastor, or a priest or deacon delegated by either of them, who assist, and before two witnesses according to the rules expressed in the following canons and without prejudice to the exceptions mentioned in cann. 144, 1112, §1, 1116, and 1127, §§1-2.

§2. The person who assists at a marriage is understood to be only that person who is present, asks for the manifestation of the consent of the contracting parties, and receives it in the name of the Church.

This is referred to as the marriage having canonical form. Since your marriage was officiated by a non-Catholic priest, then it lacked the relevant canonical form, and thus its validity hinges on you getting a previous dispensation from canonical form, as per Canons 1124–1126:

1124 Without express permission of the competent authority, a marriage is prohibited between two baptized persons of whom one is baptized in the Catholic Church or received into it after baptism and has not defected from it by a formal act and the other of whom is enrolled in a Church or ecclesial community not in full communion with the Catholic Church.

1125 The local ordinary can grant a permission of this kind if there is a just and reasonable cause. He is not to grant it unless the following conditions have been fulfilled:

1/ the Catholic party is to declare that he or she is prepared to remove dangers of defecting from the faith and is to make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church;

2/ the other party is to be informed at an appropriate time about the promises which the Catholic party is to make, in such a way that it is certain that he or she is truly aware of the promise and obligation of the Catholic party;

3/ both parties are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.

1126 It is for the conference of bishops to establish the method in which these declarations and promises, which are always required, must be made and to define the manner in which they are to be established in the external forum and the non-Catholic party informed about them.

However, since the marriage has already happened, and its only reason for invalidity is the lack of dispensation of canonical form, you can petition your Ordinary to receive a retroactive dispensation, called a radical sanation, as described in Canons 1161–1163:

1161

§1. The radical sanation of an invalid marriage is its convalidation without the renewal of consent, which is granted by competent authority and entails the dispensation from an impediment, if there is one, and from canonical form, if it was not observed, and the retroactivity of canonical effects.

§2. Convalidation occurs at the moment of the granting of the favor. Retroactivity, however, is understood to extend to the moment of the celebration of the marriage unless other provision is expressly made.

§3. A radical sanation is not to be granted unless it is probable that the parties wish to persevere in conjugal life.

1162

§1. A marriage cannot be radically sanated if consent is lacking in either or both of the parties, whether the consent was lacking from the beginning or, though present in the beginning, was revoked afterwards.

§2. If this consent was indeed lacking from the beginning but was given afterwards, the sanation can be granted from the moment the consent was given.

1163

§1. A marriage which is invalid because of an impediment or a defect of legitimate form can be sanated provided that the consent of each party perseveres.

§2. A marriage which is invalid because of an impediment of natural law or of divine positive law can be sanated only after the impediment has ceased.

It is this radical sanation, or else another procedure called a simple convalidation, which is canonically meant when people speak of having marriages blessed. This means it is not a ceremony, but a canonical procedure. Therefore any ceremonies that might take place in addition can be done anywhere your parish priest and you two think prudent.

Therefore, I would talk to him about the issue; I'm sure you will be able to work out something which is acceptable to all parties.