Yes you could, but it will add some extra weight. You don't need shielded wire for this. It just needs one wire from the GTR-200 to the PPT switch. The other side can go to your closest airframe ground. My opinion is that you only want to use shielded where it is called for because of the extra weight.
I used mostly 22 AWG where the wire wasn't shielded because of the added robustness, 24 ga. is pretty small and can easily break if flexed.