Best way to power Christmas lights without nearby outlet
If you want a quiet, convenient way to power your lights, your idea of using an DC/AC inverter with a conventional 12V lead-acid battery is probably the best one. You will not be able to supply 200W in a cost-effective way using either AA batteries or a miniature portable 'power bank' for cell phones.

Doing some figures, using an approximate energy density of 35 Wh/kg and a battery mass of around 20kg, this gives you a total capacity from a single automotive-sized battery of 700 Wh. You will need to verify this capacity when you choose a battery, which may be difficult since many automotive batteries do not have watt-hour or amp-hour ratings advertised. However, this means you can meet your requirement (ca. 400 Wh) with a single (fairly expensive, but reusable) battery connected to an appropriately rated inverter. Since you will be operating the battery without immediately charging it, look for a deep-cycle type battery with a discharge count rating in addition to its energy capacity rating.

Another option which is louder and requires a different investment is a hydrocarbon-fueled generator. These are available in a variety of capacities and fuel capabilities. Many options would greatly exceed your duration requirement, but would still be usable. Be aware of the exhaust of the generator and only operate it outdoors with enough ventilation.