Take your time, the springs dont come into play until you the actual button out, a small black plastic block. There is a spring for the button to be pushed back out and then the second spring is behind the contact inside the housing.
The parts are not really available (that I could find), you can find used around though. I found one on Ebay, dont know if its still available. It didnt sell when I was watching it. I know of two salvage yards in my region that have/had the CX/GL bikes from out era.
If you do a google search on motorcycle salvage, you should be able to find one or more in your area, I would have to assume.
You shouldnt need them though for your problem. You might be able to substitute a different Honda model switch assembly, Im just not sure how the electrical stuff will plug in or not. It might just go together, you might have to cut and splice.
I had an issue about a month ago where my car mechanic lost my spare set of keys to my jeep, which also had my ONLY bike key. I managed to buy a NEW ignition lock with 2 keys off Ebay
GRIM-REAPER RACING MX
Do an Ebay check if you find your IS bad, and from the search I did it seems there are a few placed selling NEW OEM ignition switches for the CX/GL series. Got mine spanking new, put it in and worked like a charm, and best of all cost me about $30.00 from the US to Canada including shipping
BEWARE, you need a switch from a CDI bike. They have 6 terminals.
Have you tried to clean your switch?
The instructions for removing the switch and then removing the contact section are in the shop manual. I believe you place the key between ON and PARK, then depress the areas in the slots where the contact part attaches. There are some springs in there. Clean up everything and reassemble with dielectric grease.