Turnbull would be my first choice but I understand that Turnbull has stopped working on Smiths. I don't know of another shop that does first rate color case hardening.
Be sure you know what process your final choice uses: you don't want a paint job. The paint on process has frequently been used to restore Parker shotguns. It results in a flashy blue, yellow and gray streaked surface finish on the surface, but offers no actual case color or added hardness you get from a proper job.
A proper case coloring job won't require additional fitting: it doesn't add material to the parts as things like ceracote finish does.
AFAIK Turnb won't restore/polish/reblue S&W revolvers. Never did. Took too long.
We always took in the hammers and triggers for CCH work. Maybe that has changed now. Maybe he wants them pre-polished when received, he always did like that type of quick turn over work.
Worth a call to see what they're up to now.
Don't be surprised if they have a Minimum Charge as well.
CCH parts SHOULD drop right back into place IF they don't warp.
Any parts done through the 1430F process and into the quench have the possibility of that, but it's pretty much under control.
The colors are Microns thick. The hardness (case) is anywhere from nothing at all to a few .000 deep.
I'm not familiar with the 'Paint On' color process used on some Parkers. The Japanese made Repro's used a proprietary method of faux case colors. Something like what Ruger used (still using?).
A chemical coloring but w/o any heat being involved or if there is it's very minimal.
(DTR tried to get Ruger to buy him out of his CCH process in the early 90's for Rugers exclusive use on their firearms. But Ruger wasn't interested at the 7 figure price tag.)
Those chemical colorings all wear off fairly easy. The repro Parkers are not surface hardened under the false colors. They are made of a modern steel more than suitible for the guns. They do respond to the hi-temp furnace bone/wood charcoal CCH process.
Orig Meriden CT Parkers were Bone/Wood charcoal colorcase hardened.
When Remington took over, they had them Cyanide color hardened.
You can tell the difference in the two appearance wise.
Cyanide hardening seems to go deeper,just from experience and takes a longer annealing draw to remove it.