You can say "balls to the wall" without feeling dirty. It refers to the top of the sticks in the cockpit (another word that is not dirty) of a WW2 bomber. To go full speed, they had to push the sticks to the front of the dashboard, or go "balls to the wall".
It has nothing to do with body parts, and, frankly, if those body parts were pressed against a wall, I wouldn't be able to accomplish much.
“Body parts” was a little inside, “in country” joke. I just forgot, uh, no one here would get it. ;)
That said, I actually didn’t know the history of that expression. I always appreciate knowing such, so thanks!