Unfortunately this is the LAW we are fouling ourselves with, There are many non Muslim people who are closer to god as per Islam value than many others who they are “Muslim” However all you have to do is to go to an Islamic court and register your marriage there they will tell you what to do. I think all you have to do is saying “Ashahadi AN LA ILLAHA ILLA ALLAH and MOHAMAD RASOUL ALLAH” أشهد أن لا إله إلاَّ الله و أشهد أن محمد رسول الله
"I bear witness that there is no god except for God (Allah), and Muhammad is the messenger of God."'
Good luck and Congratulation