Throttle Cables

I snapped the throttle off my bike on track, so I'm replacing my throttle tube and the part that attaches it to the handlebars and into which the throttle cables mount. The cables are fine, but they thread into the mount on the handlebars. It looks like there is no way to screw the threaded end of the throttle cables into the mount on the handlebars without first detaching the throttle cables from the throttle bodies and pulling them out of the bike (so their threaded end can be spun into the threads in the mount).

Has anyone done this and does that sound right? I'm pretty certain it is, but am hoping someone knows a trick that defies the laws of physics.