Can non-Muslims have a Muslim wedding?

It depends on the other party's wishes. If it is a particularly traditional Muslim, you must ask the imam of the religious sect to officiate the marriage.

Traditional Muslim living customs and taboos are many. You must wash your hands and feet, eat halal, and even slaughter livestock. First of all, the slaughterer must be a Muslim and have washed your hands and feet. When slaughtering animals, you must face the direction of the holy city of Mecca. Direction, the name of Allah must be recited, the livestock must not be sick or disabled, and the blood must be drained. Only when all the above conditions are met, the food obtained can be eaten with confidence.

Even the food is so particular, so how could an important ceremony like a wedding be arranged by a Kafir (pagan)?