If you were to luck into a record muskie, you'd be wise to let her slip back down to the depths. Sure take a pic and measure if you can but let her go. Unless you really need the notoriety and the few dollars, it really is not worth it. Regardless of how honest you were, from that time on, your integrity would be questioned forever.
It's like any other sport or pastime, as soon as money/greed enter the equation, it's dead.