This here is the one to use baby.

WM005 Dr Manhattan's fingerprints are all over the thing.

Jakeem is this hammer's new daddy.

When you use hypersonic while this is equipped, does this mean the minimum range is 4 even if say halfing it would make it a 2?

No. Hypersonic would still halve your range for that action

THE RULE OF MINIMUMS AND MAXIMUMS If an effect says that a value (often a combat value) has a “minimum” value and the final result of calculating that value would be less, use that minimum value instead. page 18 Core Rulebook