The International Cessna^® 170 Association

I might need to replace the flap and aileron pulley's at the top of the rear door post.
Is it possible to do this without slacking all the cables?

In a word, NO. There are not only pulleys involved but bushings and with the cables under tension it would be impossible to accomplish your task. You might get away with undoing the carry through cable (interconnect). Refer carefully to the IPC as there are differences side to side with the stacking of pulleys and bushings. This is to keep the cables from rubbing each other.

I was afraid of that but was hoping there was a secret trick to it.
Gives me a chance to better inspect the cables and verify tension.

They're a pain even with no tension. As John mentioned don't loose the bushings when you disassemble. Typically you run a string attached to your cable when you pull one so that you don't twist and misplace the new cable on installation but be careful it's easy to screw things up.