With only 4” of wire to work with it would be difficult to use something like a terminal block. I guess that you will have to use a butt connector to splice it. Use a quality adhesive lined butt connector and it should be fine . If you want the belt and suspenders approach after you use the butt connector and heat it to shrink the cover you could add a 2nd layer of adhesive lined heat shrink over the entire butt connector. Can you leave a bit of a loop so that if it ever needs to be removed you could then add a terminal block?
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