What aircraft type? PA28?
Anyway, in general, by getting into a slight sideslip left or right you may be able to subtly alter the airflow over the fuselage, making the door close of its own accord. (I had a cowling access hatch lock failure a while ago. This particular access hatch has the hinge aligned with the airflow, so it was flapping about and overstressing the hinge. Not good. With a very light touch on the right rudder pedal I could subtly alter the airflow so that the hatch stayed shut. Diverted anyway.)
And kudos for telling ATC about your problem. They'll then know not to bother you with too much details, but will be able to tell other aircraft to get out of your way.