There is a shortage of people who can read the Torah in my community. There is one man who can but he has married out and is not Shomer Shabbat. If there is no-one else may he read?

This man can't read the torah. If you can have someone read without the Teamim that’s good enough, even one prompting and another reading is acceptable, if these solutions are not practical you can read from the Torah without Brachot until someone suitable will be able to read for you. If even that is beyond the capacity or your community – you can read from the Chumash.