I can speak with some authority one the subject of converting .38spl J-frames to 9mm because I studied the possible ways of doing it and ended up having one converted. I could have purchased a used 940 but I wanted a lightweight 9mm snubby and the 940 weighs about 22oz. I purchased a new scandium framed 360J (13.3oz) for my project and had it turned into the gun I wanted but couldn't buy. I've been shooting and carrying that gun for two years now and am very pleased with how it turned out.
First, on the cylinder swap, it can only be done using an older pre-J-magnum framed gun because that's what the 940 cylinder will fit. The newer frames (which all current J-frames are built on) use a longer cylinder and the 940 cylinder is too short to work.
Second, rechambering an existing .38spl cylinder is not a big deal. My gun was rechambered by Mark Hartshorne at Pinnacle High Performance. The conversion consists of boring the chambers to 9x23 dimensions, cutting the cylinder face for moonclips, and chamfering the charge holes. Because the chambers are cut to 9x23 a converted gun will not only shoot 9mm Luger (9x19), it'll also shoot 9x21, 9mm Largo, 356TSW, 38 Super, 9x23 Winchester, etc. Yes, a couple of those are higher pressure loads, but remember, not only did S&W make the 9mm 940, they also made 300 PC 940's chambered for 356TSW which generated pressures in the same range as the 9x23. These guns and their cylinders were stainless steel, no special metallurgy, and handled the pressure just fine. My gun has the same scandium frame as the M&P 360 .357mag and (per S&W) all of the .38spl/.357mag cyls are made from the same blanks, the strength of the new scandium and steel framed guns shouldn't be an issue. If I was converting an aluminum framed gun (642, 637, etc) I'd take it easy on the hotter loads in the interest of prolonging the life of the gun.
It's important to note that you don't want to shoot .38's through converted gun, the cases will fire form to the chambers and stick and +P loads will split the cases.
Third, the argument against these conversions because of poor accuracy shooting .355 bullets through .357 barrels is bunk. That one to two thousands of an inch just don't make that much difference. I've seen no loss of accuracy shooting 9mm from my gun compared to shooting .38's before the conversion. I've qualified with my gun and scored within 2 points of my score with my full size duty gun shooting the MCJA LE Pistol Qualification Course.
Finally, if you want a 9mm snub nosed revolver your choices are very limited - 940's, SP101's, Speed Sixes (if you can find them), and Taurus 905's. I carry a 9mm on duty and wanted a lightweight 9mm snubby for BUG/off duty use. The problem was that all the choices I listed above are steel and heavy, that's why I had my gun built. In addition to the caliber conversion I had Pinnacle do an action job, chamfer the forcing cone, smooth, round, and polish the trigger, half bob the hammer, and install a fiber optic front sight. I had Robar coat the cylinder with NP3 to make it rust proof and I added a set of Crimson Trace LG-105 laser grips.
Was it expensive? Yes - close to $1100 all together, including the purchase price of the gun, though it could be done for less.
Was it worth it? Yes - I have exactly the gun I wanted. It is light, accurate, reliable, very fast to reload, and it uses my duty ammo, which is hotter than the equivelant .38spl without the muzzle blast and recoil of a .357mag.
I hope this info helps and if I anyone has any questions I'll be happy to try to answer them.
Here's a couple of pics -
Perfect score - 50/50 using 115gr FMJ -