The Smith & Wesson top-break that had both top and side barrel latches was called the “Perfected Model†and were manufactured between 1909 to 1920. It had a conventional hammer, and differed from other top-breaks in that the trigger guard was an integral part of the frame.
The "Safety Hammerless" was an entirely different revolver. I would estimate that serial number 136,6xx was made around 1902. I have shot similar revolvers in the same serial number range using standard commercial 145 to 147 grain loads, which are on the meek side. This presumes of course that your gun is in good mechanical condition. Do not shoot any 200 grain bullet loads of any kind.
Pearl grips are fragile and often chip or crack if impacted. If you want to shoot this revolver very much it would be a good idea to replace the grips. Those made for "J" frame hand ejector revolvers are a little long, but can be easily altered to fit.