Why are you wanting to clean a cast iron skillet on the outside?
I remember getting in tons of trouble when I was a teenager for trying to thoroughly scrub my mom's cast iron skillet. It had taken me a long time to get it 'clean' and then I found out I'd messed it up and we had to spend forever getting it 'seasoned' again so stuff wouldn't stick when we cooked.
So I'm not about to do more than minimal cleaning to a cast iron skillet(or cornbread stick pan)now!