If you are improving a process, it's CRITICAL to start with the existing "as is" process, warts and all. But how are you going to produce a nice neat process map?
Here is a 1 minute review of your mapping software options:
Sign up for the yEd video training (a steal at $7)
Your choice. Save hours learning to use FREE software. Or spend hours learning Visio etc. AND pay every month for it.