Hi Steve,
No. The diameter is the problem. The OM 3 screw Rugers are built on the medium size frame. All the NM 9mm convertibles are built on the large frame. Therefore the NM cyls are too large in diameter to fit the OM med. Frames. You must find a mid frame size OM 357 cyl which is not difficult to find or expensive. You must find a mid frame size OM 9mm cyl.
OR: find an extra mid frame size OM 357 cyl which is not difficult to find or expensive.
A 9mm will not quite chamber in a 38 or 357 cyl; it will only go in about 1/2 way. If you hone about .005" from the rear 1/4" of the 357 chamber, the 9mm tapered case will chamber and fire reliably and safely. You must hone it so the 9mm rim extends out the rear of the chamber the same amount as the 357 rim thickness for reliable ignition.
Yes there will be some free bore in the chamber or 'bullet jump' until the jacketed bullets reach the chamber throat, but there they will be aligned with the barrel. Unless you need tack driving accuracy, you will have a "poor man's" convertible 9mm cyl. for fun and plinking. And you may be surprised at how well they shoot.