It sounds like the shark pack does not have a built in On/Off switch and the key is purely to lock the battery into its cradle.
If this is the case, you will need to either fit a suitable high current switch between the battery and the controller, or remove the battery to disconnect it completely to prevent the battery from discharging itself when it is not being used.
The controller will continue to draw ~42mA (0.042A) with the battery connected, which may not sound a lot, but 42mA is still enough to completely drain a fully charged 11Ah battery in less than 11 days!
The momentary push button simply powers the battery gauge indicator LEDs while it is pressed, and is supposed to provide a rough indication of the remaining battery capacity.
Presumably all 4 LEDs will illuminate when it's fully charged and only 1 LED will illuminates when it's almost empty.
Alan