I have my mom's engagement ring which is exactly as you are describing. The band is 4mm wide and 2.5mm thick. The diamond is a 1.24 ct RB on a size 4.75 finger. I am attaching photos of it!
I'm a size 7.75-8...but when I say LONG fingers, I mean it. I can hold a basketball with one hand and am a giantess
I am not keeping this ring for various reasons, but the band is 2.7mm with a 2 carat stone. I know it is not the width you are after, but I figured sharing couldn't hurt
Don't forget you will have to squeeze a band on too. Here they are together. Very substantial. I needed to go up a 1/4 size to accommodate both. You may have to do the same, or even 1/2 size.