I'm at work so don't have my calipers handy, but here's the rough numbers coming to mind:
A J-frame cylinder is ~1.30" diameter.
If we go with a 4-shot design, that leaves less than .50" for the center hole with ejector and the chamber walls.
If the center hole is 0.25", we've got about 0.20" for the total chamber wall thickness, or 0.10" each. From that 0.10", the cylinder latch points have to be machined in, and those are probably 0.05" deep... leaving 0.05" inside and out to hold the pressure of a .40S&W (35,000psi SAAMI spec, same as a .357Mag). If the chambers were not 180 degrees, it *might* be possible, but that moves it into a 5-shot K- or L-frame.
For comparison sake, all other things equal, a .327FM cylinder is six shots so the latch points are also right over the cylinders... but there's an extra .08" or so of space to work with.
With some crazy metallurgy work, and super careful machining, it might be possible... but honestly, for the effort and cost that'd be involved, I'd stick with a 5-shot .357 or .38 +P.
Snubs (particularly J's) are a tradeoff, but I bet you know that already. They're easy to conceal, but that means limited shots and cartridge diameter. If you really want a .40 deep-concealment CCW, the Kahr PM40/MK40 models are tough to beat: 5/6+1 capacity, 0.9" thick, an inch shorter than a J-snub, and comparable weight (16/25oz empty).