It sounds like you are cleaning the head AND cylinder.
(the head has the spark plug in it... the cylinder has the carb feeding into it)
And yes... You don't need to remove the engine to do this.
And the piston position doesn't matter.
Read the part in the post below called "General Troubleshooting and Tune Up"
about checking the exhaust port for carbon build up.
If you can easily see the piston as it describes... you don't need to remove the cylinder... If you can't... then by all means remove the cylinder and clean the exhaust port.
There will be no carbon anywhere else in the cylinder.
But the head might have some.... I scrape it off with an old butter knife (not a sharp one).
The most important part of this operation is getting the rings back in the correct position when you put it back together... you MUST line the ring ends up with the pins in the piston grooves.
And make sure the base gasket is in good shape.