S&W has a good record of providing such info (down to the store that ordered it from them).
It may cost a couple of bucks, but in the long run it is worth it.
When you become famous, and they say "This gun belonged to TromuluZ06!" and here is the documentation. your heirs will be glad you did your research.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
Life Member NRA
Life Member NAHC
Former President of the ECPT