@GinnyBee, I really want to do something like this! I was raised Catholic but we're not religious; however, my desire for a welcome-to-the-tribe ceremony is really strong.
When we got married, my husband and I eloped and we wrote a little ceremony with some favorite readings (poetry, etc) and our vows, and we had the ceremony in a park (with just us and the officient and a photographer, who also signed as our witness 😆)
I was thinking of following a similar format with a few readings and a little ceremony for his sponsors/"godparents." Then afterwards a nice lunch somewhere.
There are non-religious officiants you can hire for this (though, unlike a wedding, they don't need to be licensed by the State). I'm thinking of looking for one via one of the British Humanist organizations. This is the one I've found so far:
humanists.uk/ceremonies/
Of course, if you have a friend with a talent for public speaking, you could always invite that person to officiate, which would make it even more special.
We would want to do it after baby is at least two, maybe three months old and has a bit more of his own immune system going.