"I'm thinking of removing the extractor on my new Handi .308 as it hinders the smooth removal of brass from the chamber" This needs a bit more explaination, what problem(s) do you expierence?
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There is no "pressure" in the bore after the shot and your brass will not be pushed out of the chamber on it's own.
The brass is not to hot to touch when you lift it from the chamber, you will not burn your fingertips.
perhaps spend some time at a firing range with a knowledgable shooter or instructor who is familiar with Handis before you start to shoot your Handi rifle, and first learn the basics of shooting. These are fine and "fun guns..be careful, be safe, and enjoy them....<><....
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