Nope it won't Cylinders have to be hand fitted to the particular gun and the hand that turns the cylinder. Its a job of a qualified Gun Smith who specializes in Smith Wesson Revolvers. They are not drop in parts.
Let's not make a mtn out of a molehill. When you've tried a few you learn the main rule is there are no rules.
They can vary from a drop-in to needing timing and length adjustment.
The closer the two cyls are to the same vintage, the better the chance for a drop-in. A -2 to -6 is highly likely.
The overall cyl length is much more often what may need fitting; gas ring to frame and/or barrel/cyl gap.
Timing not so much especially when both cyls have the same # of chambers or only one chamber difference. And of course it's a simpler process if the replacement cyl has its original extractor star.
But it's not rocket science. Proper guidance from here on the forum or a book, some mechanical aptitude, a little dexterity, and the will to learn a little is all you need.
I suggest you borrow the cyl to try, then we'll know where you stand. The extractor rod in your -6 has a left handed thread, therefore unscrews by turning it clockwise when looking at the front of the cyl.
Here's an L frame 586 .357 with a 696 44 Spl 5 shot cyl that dropped in (timing and length):
The same cyl dropped into this 296 5 shot 44 spl to replace the Ti cyl:
Let us know how it goes if you try it and most of all remember it can be fun to personalize your gun,