Doesn't sound mad at all, though you may both want to have in hand what you'll say if it comes to light.
I did this nearly 20 years ago, we told no family, just a few people my now-spouse went to uni with who were the witnesses - quick ceremony, took them out to a little Italian place nearby for lunch, they left and and my spouse and I went to an art cinema up the road. It was lovely.
My in-laws found out by accident, we told them we just hadn't wanted to hear people's opinions on it yet which they told us was fair enough and later we discussed that yeah, we were in the right there - they were some of the most supportive people I've known, there was no issue with my spouse and them as there was with my family and me, but they were blunt as hell.
I've never told anyone on my side of the family, but they live on the other side of an ocean which makes that a lot easier.
I've talked to our kids about it, told them my reasoning and if they follow in my footsteps - it might sting if they do it for similar reasons, but I teach them that their personal information is their own and to be careful sharing it if they don't feel safe or comfortable. If I've created an environment like I had where the discomfort and risks of sharing it felt far greater than the benefits of celebrating with me, well, I've got to take a good chunk of the blame for that even no matter how I feel about it. If they just do it for low stress and I found out, then the apple isn't falling that far then & I can laugh about that.