There are only two cheat codes in Comix Zone, but they're both pretty useful. They're both input at the Sound Test screen in the options. Highlight the correct song number and press the C button. Once a code has successfully been input, you'll hear a voice say "Oh yeah!"
14, 15, 18, 5, 13, 1, 3, 18, 15, 6
After inputting the code, highlight the number of the page you want to skip to and press C. (1 for Episode 1-1, 2 for Episode 1-2, 3 for Episode 2-1, etc.) Then press Start to return to the title screen and begin the game. You'll arrive at your desired level after the opening story scene.
3, 12, 17, 2, 2, 10, 2, 7, 7, 11
You won't take any damage from anything, including the secret paper airplane attack. The only problem is you'll get stuck if you fall into lava, so maybe use the shortcut in Episode 3-1 to skip the lava entirely.