It goes without saying that marriage in Islam has certain conditions that have to be fulfilled in order for it to be valid. Prospective spouses should be keen to meet the conditions of valid marriage to guarantee the rights of each other and ensure the rightness of their marriage and its coincidence with the rulings of Shari`ah.
Sheikh Mohamed El-Moctar El-Shinqiti, director of the Islamic Center of South Plains, Lubbock, Texas, states: No, this is not acceptable. Among the most important conditions of marriage contracts are the testimony borne by witnesses and the publicity of marriage. These secure the future of the couple, and let the people know who the father of the to-come children is.
As for the way to contract the marriage, it is not necessary to have a sheikh or imam. As for the wali [guardian], it is required by all scholars, excluding the Hanafis, especially if the woman is young and she did not get married before, so the consent of her guardians is very important.
Therefore, the minimum one could do is to bring someone to contract the marriage and get two witnesses. You can specify the amount of mahr [dowry] at the contract or after that. As for the wali, if the woman is mature, the Hanafi school can be followed in this case; however, if she is young, then the consent of her parents or guardians is very important.