Glad to here you got the screw out.
Hopefully someone with experience taking these locks apart can help you with replacing the spring. Just in case your looking for replacement parts (spring and exterior handle retainer screws) here is a link for you:
https://www.chevsofthe40s.com/shop/search.lasso?search=Exterior+door+handleI don't think it should be too hard to remove the spring. Take plenty of photos before you attempt the repair and then proceed. If the spring is broken, obviously, replace it. If it's not broken, then a new one probably won't be any better than what you have. Here is the reason why.
If your door handle is sagging, I found that new springs don't help. I bought 4 new springs and ended up sending them back. This is why. The receiving part (where the handle shaft goes in) wears out and you get too much "lost motion". The fit is no longer tight and you get a sagging exterior door handle. If you look at historic photos of these old cars, the handles sagged probably just a few years after purchase. The exterior handles are heavy and experience thousands of up and down motions of the car for thousands of miles. A replacement of the receiving part (don't know what it's called) where the handle shaft is inserted is what needs replacing or perhaps shimmed.
Curt