Infidel 319,
The quick answer is that along with accommodating the different frame lug position unpredictable parts fitting likely will be required. I use a spare .38 special model 60 cylinder in my model 940, but it did not just drop right in. The following long winded & boring description of how my project went is my way of illustrating the problems you might encounter.
There are several dimensional problems to consider, but first remember that model 940s are collector revolvers that are worth almost double the value of model 640s. It makes no sense to pay big gunsmithing bills only to whack the value of your collector item in half. I approached my convertible 940 project willing to discard the .38 special parts and scrap the project if my 940 had to be altered in any way.
A .38 special range rod will just barely pass through my 940's barrel. I didn't think to ask the gunsmith to measure his range rod, but the fit was so snug I'd guess S&W used slightly smaller bores. However, that isn't a problem. Target shooters sometimes installed Colt Python barrels onto Rugers and Smith & Wessons because of Colt's smaller bores. Besides, you want to convert from a 35,000 psi cartridge to one that's around 19,000 psi so even if the .38 pressure rises a little it would still be way under what your 940 was designed for.
Because 940s use moon clips the gap behind a 940's cylinder is larger than .38 special head space. The 940 frame lug that stops the cylinder's rearward movement when you push in the ejector rod blocks the .38 special cylinder from opening. I had the rear end of the .38 cylinder I use reduced in diameter in a lathe to clear my 940's frame lug and create a shoulder that contacts the frame lug. It doesn't look right but avoided altering my 940. It would be easier to file a little off your 940's frame lug but then its 9mm cylinder will flop forward and back when it is open. This always gets mentioned when discussing .45 ACP/.45 Colt dual cylinder guns but somehow gets left out of 9mm/.38 special dual cylinder discussions.
In the ordinary assembly of revolvers or their rebarreling the shoulder of the barrel is lathe turned to produce a barrel/cylinder gap within tolerance. You would be very lucky if your replacement cylinder falls into place with a correct B/C gap. If you are just a little lucky the replacement cylinder will be too long on its front end and then could be shortened in a lathe. I was not lucky in this regard with either of two model 60 cylinders I tried. Both had over large B/C gaps. I just live with a .014" B/C gap with the model 60 cylinder I use. To correct that, I would have to have the front end of the 9mm cylinder shortened and the barrel set back to a correct B/C gap with both cylinders.
Random yokes do not necessarily drop into frames. One model 60 yoke I tried would not swing into my 940 frame. It was too large or didn't quite match. I did not have to learn how a yoke that will not enter the frame is fitted because the one I use fit just right and luckily also holds the .38 special cylinder back with no end shake. Neither model 60 cylinder I tried would work on my 940's yoke. They slid forward until they contacted the back of the barrel. It would have been possible to have the gunsmith stretch the 940 yoke to hold a .38 cylinder back and ream back the inside of the 9mm cylinder to match, but I had purchased complete model 60 cylinder yoke assemblies so that wasn't necessary.
Last, there's timing, or carry up. Replacing a revolver's cylinder with one for the same cartridge will more likely have correct timing if the original ratchet is used. That can not be done installing a .38 cylinder into a 940 because of the difference in head space. Of the two model 60 cylinder assemblies I tried, one was wildly out of time, while the one I use carries up like it was factory fitted to my 940. That was just good luck which you would need a lot of to have a model 60 cylinder drop right in to your 940.