Be sure to get the right test kit for the copper you pick up . . . Salifert, from what I'm told, works well with ionic coppers such as Cupramine, while API works best with chelated coppers such as CopperSafe.
(And don't use Kordon's "Safe Copper Aid" - it's diluted to the point of near-uselessness. Took three and a half bottles to bring a 75 gallon QT to therapeutic levels.)
A partial water change isn't likely to hurt - but remember not to rush it, which can be tempting in situations like this.
~Bruce