Colt no longer does any work, including bluing on their older models made prior to the current new stainless guns.
There are VERY few places that can be trusted to do a Colt quality re-blue job.
These are top professionals who can do a factory level blue job without over polishing the gun and removing stamps or rounding off edges and leaving ripples in the flats.
In no particular order.......
Glenrock is famous for top of the line bluing and are used by many custom gunsmiths who want the finest bluing on custom guns.
The Custom Shop IS NOT THE COLT CUSTOM SHOP. Colt once listed them as a possible source of Colt repairs and refinishing.
The pictures on the site look good, but reports are the prices are very high.
Ford's has a long time reputation for being able to do a Colt level "wet look" Colt Royal Blue as used on the Python so a Detective Special should be no problem.
They did have a problem a few years ago but apparently have correct it.
Precision appears to have an excellent reputation.
I recommend talking to these people and picking one.
Be sure you discuss that you want a COLT factory level polish job. There's a big difference between a typical gun maker's factory blue, and a COLT factory blue.