Welcome to the Forum,, (sorta!)
Ok, in general,, you need to be a bit model specific. Old Models,, (3-screw guns,) and the New Models have different enough dimensions,, in fit to where they don't interchange. Now that's out of the way,, let's discuss the New Models only.
Basically,, the biggest thing is to match the OAL of the cylinder. Measure from the rear of the ratchet, to the front of the boss on the existing cylinder,, and look for one that's the same,, or a few thousands longer. If the same,, most often, they will drop right in. If a few thousands long,, the boss can be CAREFULLY honed to allow it to fit. Timing is most often not an issue,, but alignment should ALWAYS be check prior to firing live ammo.
I'm thinking the cylinder diameters are the same for the Blackhawks & the Flattop Blackhawks so that shouldn't be a problem. Since you mentioned stainless,, he will not find any OM stainless cylinders,, because there were never any stainless 3-screw OM's built. But the NM's, in stainless should all fit as long at the OAL is the same.
Frame sizes,, the Blackhawk is a larger frame than the mid-sized Flattop frame. But I do THINK the cylinders are the same. I don't have a Lipsey's FT to compare any with. The Blackhawk frame size from 1973 to current Blackhawks are the same.