The problem is easily solved by saying, "People who drive without a seat belt take their lives in their hands." A shift to the plural often takes care of the problem, but of course you must make your nouns and verbs agree.
If you are serious about addressing this problem, I suggest that you develop a guide to non-sexist language for your writers, especially your headline writers. I've noticed they have a particular need for one. I realize that getting used to using non-sexist language is difficult, especially for older people, but I have great faith in the editors and writers of The Times. I know you can do it if you want to.
M. JANE GEBERS