As for whether it could hurt the baby, I'm not a medical expert, but I can tell you that my in mother's generation, nearly everyone wore a girdle through pregnancy. My mom was (comically) amazed that she couldn't find me a maternity girdle when I was pregnant. (Why she thought it was her place to get me such a thing to begin with is a whole other story...)
If you're worried about the girdle, why not use a belly band? They're available, and not controversial. I used an elasticized one when I was pregnant for back support, and my Asian friends use long swaths of cloth wrapped around. And if you wear a straight cut sheath dress (still chic, but not curve-hugging) to the baby blessing, that plus a belly band may be camouflage enough to protect your secret a little longer.
I do wonder, though, if you have thought through what will happen when everybody does find out. I can understand, especially after a miscarriage, wanting to make sure this pregnancy has "taken" before letting everybody know. But if you wait much past the 3 month mark, you may inadvertently hurt the feelings of those who would like to celebrate and support you. And believe me, I do know that in some families the line between "supportive" and "meddlesome" is a fine line, or a non-existent one. (See section on girdle above.)