There currently isn't a cheat device for PS1 games emulated on a PSP. The best cheat device is CWCheat 0.9.1 RevB and it only covers PSP games. However, according to their forum, they've been thinking about expanding the library to PS1 games. You will just have to wait until they release the official 1.0 version when they have successfully debugged the program. Then they'll probably work on the PS1 cheats.
actually there is a cwcheat for POPS(psx) and it supports gameshark codes and codebreaker codes... to start it is just the same as starting in a umd...
psp35 is right. The latest CWCheat, 0.9.1 RevB, includes the plugin for PS1 game support. So KonoStarX start cheating!
http://cwcheat.consoleworld.org/ To install it extract the files from the rar/zip archive and put the "seplugins" folder in the root of your memorystick. Enable the plugins in the recovery menu and your set. When playing a game holding the Select button will bring up a cheat menu.