Well, as an update, I've just successfully swapped in Planet Bike's clip on the Hotshot. I got the parts that I needed free from my LBS's spare parts bin (yay!). Examining the Planet Bike clip, I noticed the C-shaped cutout for the one-way ramp system (for lack of better words). The Cygolite clip is similar, but mirrored to slide in the opposite direction.
To remove the clip on the Hotshot, I had to defeat the one-way ramp with a push from a safety pin. To install the Planet Bike clip, I filed off the one-way ramp, which is now a hindrance. That is, since Planet Bike's clip ramped in the opposite direction to the Cygolite, it's preventing you from pushing the clip in, instead of preventing the clip from accidentally pulling out.
There's a very minor size discrepancy, which means that the Cygolite is now slightly off center. Also, while the clip is in pretty tight, the clip is actually very slightly smaller and doesn't fill in the entire space. I hope it will stay put.