There is a forum further down - CBOM - that is all about this. Yes, same chord shapes, but they comein different sizes. Because the frets are further apart near the nut of a long neked OM, some chords that you use on the mando are a bit of a stretch on the OM. I have a similar itch, and my search is leading me toward a tenor guitar. They are 4 string instruments that can be tuned like mandolas or OMs.
"First you master your instrument, then you master the music, then you forget about all that ... and just play"
Charlie "Bird" Parker