All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The presence of a third party other than the bridegroom and the guardian of the bride, and the witnesses according to the majority of scholars is not a condition in conducting the marriage contract. What is considered in the validity of marriage is the consent and acceptance by the bridegroom and the guardian of the wife, and the presence of the witnesses.
There is no harm if a third party is present like the court registrar, the judge and the like. If they are present, then the matter is one of the following:
1- Either the judge or the registrar are authorized to act on behalf of the guardian of the bride and in this case it is not permissible for a woman to be conducting the marriage, because it is a condition that the authorized person appointed on behalf of the guardian of the bride to be a male, like the guardian himself.
2- Or that the judge or the registrar are there just to say the formula of acceptance and consent between the parties of the contract, as it happens in many countries. The contract is correct this way but a woman should not be doing this, as this necessitates her to attend ceremonies held by men, and she is not fit for this.
Finally, it should be noted that a woman should not marry herself, rather her marriage is not valid without the consent of her guardian, according to the view of the majority of the scholars. The evidence is that 'Aa'ishah narrated that the Prophet said: "Any woman who gets married without the consent of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid." [Abu Daawood]
Allaah Knows best.