When I need to say something I'm embarrassed about, my strategy is to say it in as few words as possible, to curb over thinking and get it over with fast, and as bluntly as possible, so it won't be misunderstood causing me to have to say it again, and so it hides my embarrassment somewhat by showing some amount of confidence.
Also, waiting for the best time to say it isn't always the best thing to do, despite how logical it seems, because it gives you too much time to gather self doubts and decide not to do it. You can, of course, gather confidence that way too, but in my experience it's not as easy. I recommend saying it the next time anybody can be there to listen.
This advise is of course, based on my own personal, autistic and somewhat tone-deaf experience, and based on the assumption that you will be accepted, which you seem to indicate you would be.
At the very least, it'd create a discussion for you to talk about what you need to, so if you think it'd work for you I think it's worth a shot.
My username? O
My real name?