Despite what the jewelry industry would have us all believe, when two people agree to marry each other, they ARE ENGAGED.
It's not a requirement, it's just a tradition! (If you don't cut a cake, are you really married?)
People look at me weird for not having an e-ring, too. I have no desire for a ring.
I totally hear your frustration. Some people always have to be dorks.
Yes, tell them you are engaged!!!