What you are planning to do is a good step in keeping your steppers working optimally.
First, the credit wheel will come off now, just wriggle it a little more aggressively and it will come off.
Second, Its a good idea to undo the screws that hold the unit too the front of the lite box, this will give you more access to the unit.
The switch stacks can be unscrewed but notice there are two stacks either side of the mounting bracket. If the individual bakelite spacers are loose I put one screw back through all of them and keep it all together. I also am suspicious that the vertical switch behind the first switch stack has the been assembled correctly. Its a minor thing but the outside switch has a plated back blade that seems to be inverted in your picture.
The next step is to undo all the springs including the middle one that keeps tension on the cog wheel. I use pliers to remove the sprung arm on this one and let it uncoil about three times usually. Its easy now to remove the coil stops and the coils and all the mechanical parts can be taken to a bench for a good clean and polish. I usually put all the small parts in the tumbler for a day and the springs will clean up like new.
I get spring replacement kits from Steve at PBR and replace often it they look like they have stretched or kinked. The coil stops should be changed if the contact surface is mushroomed or looks damaged, otherwise they go back in 95% of the time. I clean the metal surfaces by degreasing in my ultrasonic or just use a metal cleaner and elbow grease.
Lastly shine up the switch blades and contacts with a dremel wire wheel. The one Nick Volta uses is good I am sure but any of the dremel brushes that the box store carries is fine.
Lastly I minimally teflon lube the metal areas that rotate against each other as I rebuild the stepper.
Takes less than an hour to disassemble and the same to put back together after cleaning.
Good for another 10 years.