fusty, i was in much your situation - a ds, not Jewish and a Jewish father. Slightly different in that my DH himself had a Jewish father only, was brought up atheist and had converted via the Reform synagogue before we met. He was a fairly strong believer though only mildly active in the synagogue. We agreed to bring ds up as a Jewish boy.
We did have ds circumcised, rather later than it should be done by tradition, as we were waiting for an appointment with the person recommended by our rabbi- a doctor with years of experience who used anaesthetic etc.
I was influenced by feeling that ds was already going to struggle to be accepted as Jewish, and therefore that he needed to be as Jewish as possible IYSWIM. However, I fully understood that being circumcised does not make you Jewish. DH was also very pro.
It was awful. Nothing unexpected happened, like an infection or whatever. But he screamed. I remember it so clearly. DH, who was in the room, feels that the scream was more because of the position ds had to be held in, and the general interference. I can't know. Logic tells me it was rather more likely to be about the operation itself!
He had just started smiling, about 3 days before the operation. He stopped smiling for a day and a half afterwards
It was made slightly worse for me, perhaps, by the fact that instead of a big family bris with lots of support, we were on our own at a GP surgery. But nothing changes the central fact of what you are doing to a child.
I am influenced in my dislike of the procedure by the fact that by about two years later, dh had lost his faith completely and no longer wanted to be involved in Judaism. I felt then, and still feel, that I let my son down, and that for not very coherent reasons I allowed something that goes against what I feel is right for children, i.e. that absolutely nothing medical should happen to them unless it is the best possible choice for their future. I also have met Jewish women who have chosen not to circumcise their sons, since that time. (I haven't sought them out, by the way).
This is an unrelentingly negative story, sorry! I can easily imagine you choosing another route and being happy with it, plenty of people are. In fact all the men in my family are circumcised too (very fashionable in post-war times). I think it is obvious that I would not choose the same route again, nor would I ever recommend what I did to someone else. However, every family is different. HTH and best wishes.