Fully Disable PrntScr Key

You should be able to disable PrntScr on the console with a custom keymap. On archlinux the procedure is as follows (it should be similar for other distros):

1. cd /usr/share/kbd/keymaps/i386/qwerty
2. copy your default keymap to a new file: cp us.map.gz personal.map.gz
3. gunzip the new map file: gunzip personal.map.gz

4. edit personal.map using your favorite editor:
   switch to a tty, run showkey and press PrntScr to get the key code. On my system it outputs:

   keycode 99 press
   keycode 99 release
   

   so PrntScr code is 99. Add

   keycode  99 = nul
   

   to personal.map

5. gzip the map file: gzip personal.map then run loadkeys personal to load the custom keymap then hit PrntScr to test the new keymap.
6. make it permanent by (creating if not present and) editing /etc/vconsole.conf: replace KEYMAP=us with KEYMAP=personal.
7. reboot

The above works only on console, you will have to disable PrntScr also in X.
One way to do that is to comment it out in your X keycodes file (the one corresponding to your keyboard - linux uses /usr/share/X11/xkb/keycodes/evdev). Key code is <PRSC>, just comment it out (add // in front of it) e.g. replacing

<PRSC> = 107;

with

// <PRSC> = 107;

completely disables PrntScr.