You have two choices. You can wait until someone seeks you out, or you can be forthcoming. If you’re forthcoming you have the opportunity to earn trust. If you wait until you’re hunted down by your co-worker you demonstrate a major lack of readiness for responsibility.
Make a habit of hiding the truth, and you convert your co-worker into a status hunter. This not fun for anyone; neither ambushing you in the hallway, nor being ambushed, is a particularly enjoyable experience.
Either way the news is delivered, and you can’t hide forever, so why not choose to be a leader?