Buy an infant nasal aspirator. You can find it at any drug store. It is safe for infants AND cats and kittens. I have one on hand all the time in case my cats get an upper respiratory infection and their noses get clogged.

When you use it, squeeze all the air out of it before inserting it gently into the cats nostril. It should help get out any gunk that's there.

Another thing you can do is bring the cat into the bathroom. Close the door and turn the hot water on in the shower. The steam will help loosen any gunk in the nose as well.

Good luck.