Rolex VINTAGE 1920-1930

Hello guys, I am new to vintage watches. Never even tried one on my wrist, but yesterday the lightning has striked me when I saw Rolex cushion-shape case from 1920's on Ebay. Beautiful numerals, hands, easy to read minute scale, so simple charming and classic, but there is a problem case size is 31.5 mm. The watch this size will look silly on my wrist so I decided to look for another with your help.

I am looking for cushion-shape case Rolex from 1920's-1930's with a bigger case. To be frank with you I am big fan of Panerai from 30's with the same shape of case so I want to give Rolex a try.

I need watch to be fully functional, tested, serviced, it has to be full original (all parts have to be original). I prefer black faces. BLACK FACE ONLY and CUSHION-SHAPE ONLY.

Please contact me if you have something interesting, because I am about to buy that small watch from Tokyo that I will never be able to wear because of the size, just for my collection.

Does anyone know if Rolex produced 40 mm watches back in 1920's?

Please PM me. Thank you.