Take a look at the LMC
page
The all steel turn signal shown was changed to a plastic unit like you have. I don't believe your truck used a spring. No spring as long as the correct cam/canceler and other parts are correct.
Also you said the color of the "wires" changed to brown. No big deal, BUT did you mean to say "wire" not "wires". Only one wire.
I will wait for pix to confirm. If you do use that spring, it seems it is a very low pressure, small wire, spring. If you are placing the so called "retainer" correctly and all other parts correctly, I don't see how it would break the bearing. But I don't have pics to see what "breaking the bearing" is. If you feel a large spring force when installing the wheel, something is wrong with your stack up of parts.
Probably need to see a layout of your parts the way you are installing. Then maybe someone will spot something. Work on getting pix posted.
Installation videos of 1963 Chevy truck steering wheels do not show a spring. The bearing stays nested in the plastic switch housing....and probably held in by the cam/canceller skirt.
I will add no. 3 to the possibilities.
1. Wrong parts
2. Wrong assembly
3. You think you have the correct parts because it's hard to find info. I agree you and I would think they are correct because they were included. Some heavy duty spring were used on tilt wheels. There is the possibility of a column swap done by a PO. Looks the same but different. The new style plastic housing T/S probably mounts in same holes as the older all metal turn signal parts. Due to one casting/machining design for all Chevy and GMC trucks of that era, didn't change holes, just designed a modular switch. This is evidenced by the T/S fitting both Chevy and GMC.