The serial number dates it to 1956. It would be a Chiefs Special Airweight, which became the model 37 when S&W began stamping model numbers around 1957.
The guns hand is likely worn. It's an easy fix for an experienced gunsmith.
It's unlikely S&W will give you free shipping or a free fix for a 50+ year old gun.
As long as you don't shoot it by very slow cocking it, it will not be an issue as it more than likely locks up fine with a normal trigger pull.
Jim
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