My model 36's SN is about 20 less than yours. When I bought it new years ago it started out with extraction issues that turned into ejection issues once the extraction one was solved. When the call to Cooper went sour I worked out the extraction/ejection problems myself. My notes from back then mention buying spring stock from the hardware store but don't mention the size used.
How does your new rifle's magazine work? Fwiw, I hope your rifle comes with an extra.
If it's been shot much during it's life, it just might give you no problems. Mine proved to be a winner. After reworking the magazine to fit as it was difficult to extract or insert.