Just because there isn't a SAAMI industry standard for .40 S&W, that doesn't mean some small ammunition company might not decide to try and sell a hot-rodded .40 load that they label as "+P" for marketing purpose & advertising.
Personally, I wouldn't consider shooting any ammo in my own .40's that wasn't produced to recognized, acceptable industry standards.
Of course, I also only use ammo made by one or another of the major American ammo companies (who have acquired some experience in making .40 loads for LE agency customers).
Congrats on the CS40. I'd consider replacing the recoil & mag springs (with factory springs) before shooting the gun.