I'll agree that the shipment from the factory of your revolver was probably made some time in 1901, and probably in the later half of that year, based upon several relatively nearby SNs having known shipping dates. But SNs don't track too closely with shipping date, so 1902 shipment is always a possibility. Yours probably has the caliber "38 Special" stamped on the barrel. That started around SN 7500.

The Model of 1899 is a somewhat historic revolver for S&W as it was the very first built on the K-size frame, and is the direct ancestor of many millions of K-frame revolvers made since. It's not incorrect to say that S&W owes most of its success to the Model of 1899, as the K-frame revolvers have, for most of its existence, been its mainstay for sales throughout the world. It was followed by the Model of 1902, which incorporated some mechanical improvements. There were approximately 21,000 1899s made in .38 Special, and somewhat fewer (about 5,300) were chambered in .32-20 (called the .32 Winchester back then). In the 1900-1901 period the U. S. Navy and U. S. Army each purchased 1000 Model 1899s, but it was not adopted by either for military service at that time. Yours is not in the SN range of those military purchases. Examples of those military 1899s are the most desirable to collectors. A few Model 1899s were made up in "Target" style with adjustable sights, and those are also desirable.

1899s are always readily identifiable as they do not have a spring-loaded support lug on the barrel ahead of the extractor rod tip as do all later models. Be very careful to not lose the knob on the end of the extractor rod. Original replacement knobs are all but impossible to find.

Yours may well be in shootable condition and it can be fired safely with standard velocity lead bullet cartridges. Even so, I would not recommend firing it. I would also not recommend you go probing around its innards with a screwdriver. If you break something, it is likely that it cannot be replaced. At its age it deserves retirement memento, not shooting, status. It is older than about 99.999+% of humans still alive. Don't even think about having it refinished. Just clean and wax it.