Of course it is possible! Who told you it’s impossible?? And you do not have to become a muslim. As I understand you are the bride-christian, and the groom is the musim, right? So it’s better if your guy goes to the Shariah court, they will tell him exactly what they require, and they barely speak English there. They for sure will ask for your passports. Then they will ask a letter from your that you are Christian and want to marry [NAME], muslim. They may ask you a permit from your Dad or your brother. If no any Man from your family is available here, they may ask your for the letter, explaining the situation. All the documents and letters from your side must be translated into Arabic. Then your guy bring all the paper to the court, they arrange the Date for the marriage. It can be in a next couple of days, or any other day on your choice. Then at the day of the marriage you guys come to the court, they first check your documents again, verify your ID. Then you go to the second floor, to see a Judge, who asks you how much money you want before Marriage and how much you want upon Divorce. Be ready with the numbers. Then he will bless you in the name of Allah, and that's it. All the procedure takes about 40-45 minutes. Bring 2 witnesses with you. Khalas. Done. You can arrange the reception/party the same evening at home or in the restaurant… Nothing complicated. Everyone can do it...:)
Good Luck!!! And Happy marriage to you!!