No, I play this on a PSP, but I use RemoteJoy to display it on my PC. That way, I can record the video using Fraps or Bandicam. The HP Hack is done with CWCheats, search for that on Google an you'll find a lot of info :D
I can't remember if my stick was also bad when I recorded this. At some point it began to work a little bad and I played for months that way until I decided to disarm it and clean it and that solved the problem. But yeah. it is a pain when you press left and the character goes walking insted of running.
Well, you need to overclock your PSP from de VHS menu to have the best performance, but even if you don't do it, RemoteJoy does work nice, and the FPS drop is minimal.