Camera Electronic Shutter
The kind of CMOS camera modules you are asking about all have global shutters (electronic shutters, not focal plane shutters). You control them through their bus, typically some sort of serial bus like e.g. I2C.

You can find modules where you have control over both frame rate and shutter speed.

I very much doubt any camera module has a separate shutter pin. You need to implement the bus protocol anyway, or there would be no way for you to get the image data...