The charger may not operate properly without a battery connected. It may present an extremely high voltage, or none at all. Also, 1A is barely anything, especially on a 6V system. If it were 12V, there are plenty of power supplies out there that would feed the system enough to do everything except turn the starter. I'm not aware of any 6V solutions, though undoubtedly there are some out there.
2005 Yamaha Zuma YW50, 2009 Kawasaki Super Sherpa KL250