I'm not sure what the the TT screen is made of, therefore I would recommend chain drilling it rather than using a jigsaw or hacksaw. You'll probably find the noise goes way up but you can always screw a little blank over it if it doesn't work.
You might want to consider fitting some spacers under the screen mounitngs, that usually gives you a better air flow without the turbulence, this is a common fix on Tigers and similar bikes.