Sorry - got it smelted once I broke off the engagement. I only know the specs because the jeweller annotated them (it was a custom model).
It’s also relevant to note that 4mm was only at the upper shank - the lower was thinner.
I could not find ring heights because search engines indicate width instead, even when I search for height.
That’s because that dimension is referred to by multiple names, including “depth” and “thickness”. I also gave ChatGPT a check to see if it could refer me to links that could help you, but it was also messing up with the dimensions.
I think that your best bet would be to test it with a jeweller, and see what feels comfortable in this regard.