I would like to buy a new DSLR camera but I'm concerned about security. I was wondering if there's a camera on the market that doesn't have built-in wireless connectivity to it or has an option to physically disable it.
As far as I know, they all allow disabling. In fact, all the ones I have direct experience with require specifically enabling Bluetooth or WiFi in order to use it.
My Nikon D7200 supports WiFi but it's default disabled. Simply enabling the WiFi on the as shipped camera does indeed put it in an open insecure mode, but the Nikon App will allow you to change it to a secure WPA2 protocol.
The biggest potential security concern with a camera, especially on a phone but also newer DSLRs, is recording GPS location data in the pictures. It's a nice reference value in principle, but telling everyone where you or your children live is probably not a good idea. Fortunately most picture sites strip this EXIF information out, but be aware that it exists.
Per Scottbb comments:
My answer assumes that your interest is in personal security vice conforming to corporate security environments.