I don't think there's a skip level cheat code, but there are some other cheat codes. I've added the list to this post.
The level you're describing sounds like The Escher Labs, which is in Episode 2, Mission 5 (named after the artist M.C. Escher who's art inspired the level design).
What you could do is start episode 2, then enter the cheat codes nbdeity and nbkeys. Then it would be a lot faster to run through the levels you're already played since you won't have hunt for the keys or worry about killing the enemies. I think you have to enter the nbkeys code each level.
You just type these in game (not into a console or text chat or anything like that). Be careful with cheat codes. Some of them can't be undone:
Type the codes in-game just like in Doom:
nbdeity - toggles god mode (can still take damage over 100 health)
nbkfa - give full health, ammo, keys, and weapons
nbkeys - gives all keys
nbshooters - gives all weapons
nbdeathless - gives full health and armor
nbfastfingers / nbff - doubles fire speed (this will stack!)
nbregularfingers - sets fire speed back to normal
nbponcho - toggles lava suit for 300 seconds
nbhot - toggles superhot mode for 300 seconds
nbspoder - toggles climbing powerup for 300 seconds
nbfrog - increases jump height by .1 each time it's typed
nbman - resets jump height to normal
nbwoohoo - toggles a janky slow motion mode
nbgotta - toggles double movement speed (also affects some vertical motions such as jump pads)
nbreflect - mirror mode (cannot be toggled off)
nbullets - Infinite Ammo
nbufo - Fly Fly Away