Hello Kaceemissouri,
Let me be the first to welcome you to the Smith & Wesson forum.
To answer your question, NO.
I just did some testing;
The 4040PD magazine is based on the 3913 single stack - Lady Smith and NL variants.
The CS-40 magazine is based on the 45XX series with a small spacer in the rear of the
mag to take up for the shorter .40 S&W round.
Also similar is the 10XX series but have a tang on the side of them that will not allow insertion.
All that being said, the 4516 and 4506 series will work,
BUT the rounds can float from front to the rear in the mags.
They will function perfectly though and also lock back after the last round is expended,
I do it all the time at the range.
Does anyone else see a potential problem here?
Oh and by the way, I would still buy the 4040PD.
It fits all the 3913 leather and you can swap the Hogue grips with the 3913 and it is also a great firearm.
Regards,
BM1