Others have already pointed out it is pretty much impossible to do in-camera unless the camera is a smartphone or really old and already does not record EXIF it at all.
Now for a solution that's workable and might not be such a hassle.
I presume you own a computer and do not just go to your customers, SD card/flash disk/camera at hand.
If so, there are very many programs/applications that allow you to strip metadata from images in batches (many images at once).
Google search for "batch remove metadata images" and select some application that does that.
My personal recommendations (no relation to any of the products at all) are exiftools and the solutions offered in This superuser.com question (How can I remove the EXIF tags/metadata from several images at once?).
Integrate the step of removing the metadata just after copying them from the camera.