Check out this new design throttle lock.
ATLAS Throttle Lock
These just became available for order this month I believe. Looks like they could fit the Hawks easily without hitting the tank or the fairing. It basically clamps on the tube, so it rotates with the throttle. When you want to engage it just click the button, and it opens up and binds on the housing, holding it in position. These are made completely in the USA and are all metal.

My father might order one for his '05 Hawk, the NEP works on mine but not on the newer ones without hitting the fairing.

 

Those look rather large, as far as throttle locks go. Check out the Vists Cruise throttle lock. It's a friction lock as well. It is super simple to use. Once installed, it looks like it's supposed to be there. A flick of your thumb and its locked. You can easily overide it in case of emergency. Mine doesn't hit the tank, but others have mentioned it barely touches at full lock, which is remedied by a little sandpaper. There is no way it will hit the fairing.

You really don't need a throttle lock that rotates with the grip for our bike. Even at cruise speed on the highway, you have barely turned your wrist.

 

My father has a Vista cruise on his Magna, and claims it doesn't work on his Hawk. Maybe he isn't creative enough! The Atlas is pretty big but it is all at the bottom, so there shouldn't be any interference with needing to reach around for the start button or the kill switch.

 

Yikes! Paid $20 for my vista cruise....

 

I have this one. NEP Motorcycle Cruise Control Throttle Lock for Dual Cable Throttles 7 8" CC3 | eBay

Been using it 15yrs on this and cbr600s. Works perfectly and you could buy a nice set of gloves for the money of the atlas.

Kinda seems like a lot of mechanical mayhem for a simple problem.

 

I need to look further at this for my wifes Ninja 650R.. as the Vista Cruz I like so much for my bike and others does not work on hers,, you have to use their universal version which is cumbersome and unsightly or modify a standard model and screw it to the switch housing which I'm considering.