I have inadvertently actuated my "panic alarm" several times from what I'll call a "pocket press". As you're aware, if you hold the panic button for a few seconds, your horn honks for some unknown amount of time (maybe someone can help with how long - probably 1 to 3 minutes). My neighbors have come to love me with my horn blazing in my driveway.
I decided I was going to attempt to fix this but I pleasantly wound up with a different solution than I expected.
I first took apart my fob (spoiler alert in the first photo):


To get the fob open, put a flat blade screwdriver in the opening as shown. Gently rotate to pry apart the fob. When apart, you can disassemble and wind up with this bunch of parts:


I considered slicing part of the rubber out to prevent the panic button from being pressed. I also considered cutting the legs of the button for the panic button on the circuit board. Both of these were what I'd call "destructive solutions". Instead, I removed the outer button by pressing the tabs inward with a screwdriver. The part came out easily:


This ended up better than I expected. The panic button is still accessible by pushing your finger into the white rubber circle. You can feel the button press but it is much more difficult to inadvertently press the button. If you don't mind how the fob looks when you are done, this is an excellent solution. If the look bothers you and you don't mind completely disabling the button, I'd recommend putting a spacer under the outer plastic button that's slightly larger than the rubber white circle. The finished product: