Pdoz - just buy PSW inverter for your shed. 300W Samlex costs $160 and will run any electronics. I would also get 12V lights, to avoid keeping inverter on stand-by 24 hours. It drains quite a lot of energy on standby, without any loads.
Yes, it had crossed my mind that it would be cheaper to buy a small sw inverter for the ebike than replacing the battery / charger on the bike if I found my modified sw fried them!