Hi Traveler,
The vintage Whizzer company actually had a tool to remove the "C" clips and the part number was SPT-2223 and called a spring depressor. It is simply a peice of tubing with a door cut out to allow access to the "C" clip, and you had to use long nose pliers to pull the "C" clip out. I just normally use a large screwdriver on the rear of the retainer washer and push the front of the washer with my finger to keep the washer from binding on the valve stem while it is being "depressed". Once the retaining washer is lower than the slot in the valve stem the "C" clip can normally be pushed aside easily. The trick is to use a LARGE screwdriver, because it won't slip off the edge of the retaining washer as easily.
To me removing & re-installing the valves, springs, washers, & clips is the easiest part of doing the "valve job" on a Whizzer. However I have worked on hundreds of cylinders, so the repetition might make it seems easier.
On very common mistake I continue to see is the "C" clip installed upside down. The flat edge of the clip is located away from the washer. If installed correctly the rounded edge sets inside the retaining washer because the washer has a rounded area that fits the "C" clip exactly. If installed upside down the "C" clip will rock and widen the slot [groove] in the valve stem and cause extra wear on the "C" clip. About 75% of all the motors I work on have the clips installed wrong.
I have a bunch of heavy duty [high performance] valve springs to fit the motor if needed.
Have fun