First, the person who said don't shoot it is right. For one thing, why would you (risk it)? It's largely a defunct or at best very small niche round, hard and expensive to find ammo for and with so many other choices out there to shoot. At the very least, find out if it is a) all original or b) at least been fixed with period-correct parts, and c) have it checked by a gunsmith regardless, but especially if remotely considering shooting it. A lot of these .41s have been "humped" up by now, rendered as mixmsters with 2nd Gen .357 or .45 Cylinders and replacement barrels--nothing wrong with that, but those are not worth "lettering" with Colt. However, it looks like yours was probably largely untouched, as your guess is....so yours may be worthwhile. That "lettering" means, for a couple hundred dollars, Colt will send you.an authentication letter showing the original provenance - its basic configuration as of shipment and DOB (DOM) based on serial number,...and where originally shipped to (usually a store or distributor). Some feel the .41s aren't worth the lettering, but again if otherwise found to be all original or period, it wouldn't hurt and could help should you decide to sell.
The .41 Colt was fourth or fifth in popularity behind the original .45 Colt, then .44-40, .38-40, and .32-20, but ahead IIRC of the .44 Russian and rare and 20th Century-only (about the time of your gun) .44 Special, very rare .38 Special and ultra-rare .357. A whole lot of other esoteric calibers were also offered in limited numbers. The caliber/cartridge does have some history. I forget which, but Billy the Kid or John Wesley Hardin was known to carry a .41 in the late 19th Century - as chambered in the 1877 Colt, it's first try at a double action.
Can't help too much on value, someone else will chime in, but if the gun has no "special provenance" (like owned by Teddy Roosevelt or used by Bonnie and Clyde...and the Colt letter wouldn't usually indicate end-user/buyer anyway, so you'd have to stumble upon that sort of thing differently)...but otherwise is all original and fine shape,--my guess is maybe $2,000-2,250, $2500 tops. Being a .45 or .44-40, .38-40, etc., would add $300-500 to that...again for an un-messed with example but still missing most of the original finish as yours appears to. But...I could be off by a third in either direction!
Btw, very cool gun! I'd leave it alone other than a check and superficial cleaning, and just enjoy it. Show it off to friends and family. A piece of history--and sounds like family provenance even if no other special background.