The HTC Vive controller can be identified by its model number: 2PR7100. It is a first generation motion controller released by HTC on April 5th, 2016 as an accessory part of the Vive Virtual Reality set.
Short of getting the screws from HTC directly, the best option I could think of would be going to a hardware store to have someone size them and either replace them, or give you data to shop around for.
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