Your coworker was unquestionably rude to mention that your speech sounded like you were wearing a retainer.
That being said, according to you, your speech has been affected by your dentures. If you really don’t want people to know about your dentures, you need to practice, practice, practice, until you can figure out how to compensate for your new mouth shape and make it an automatic, ingrained, part of your speech. I had a mouthpiece in college for TMJ that dramatically altered the shape of my upper palate, so I can sympathize with the difficulty and frustration, but know that you can overcome your articulation issues.