I think it helps not to use euphemisms I don't like them at all. I had a friend in our younger years, whose mother gave her such banal advice along these lines "keep your hands over your penny" what kind of nonsense is that, presumably she meant don't engage in sexual foreplay, "well say what you mean then"
I had boys and once they got to the giggly nursery/school age, willy and bottom figured a lot, how small boys love lavatory humour kept them amused for ages. So I suppose when they were at that age "willy" was used mainly by them, but they always knew the correct word.
I think having a granddaughter, was a game changer. I'm trying to recall instances when there would have been a time when I had to refer to any of that, very occasionally. I think I'd refer to the "genital area" which I suppose isn't specific, as in when we went swimming , "make sure you dry yourself everywhere". We've had several discussions about periods, but I can't remember having cause to use the anatomical names, which she's well aware of. My older step granddaughters and sons, don't beat around the bush depending on the context of the conversation in using both penis and vagina, none use euphemisms, they don't seem to share the embarrassment of previous generations. Their ages range in the twenties and thirties. Possibly, they're typical of that age demographic.