You may want to look into a
MOSFET R/R upgrade while you're at it. Due to the design differences, they're more efficient, which translates into higher output at idle, steadier output through the whole range, and less waste heat produced (which in turn means more life out of the R/R). The stocker can fail open or closed - one way just doesn't generate enough power, the other way puts out too much and fries your battery.
Most of the Shindengen MOSFET R/Rs have (fairly expensive)
Furukawa connectors. You can replace the stock harness connector, buy a PnP adapter, or rig it up with generic female terminals (losing its waterproof seal in the process). Or the FH016 R/R off the '07-'08 ZX6R has wire pigtails instead, so can install any plug you want (e.g. the OEM Ninjette connector).