If the sheet metal duct is not formed properly the metal will flex and cause a popping sound. Normally cross breaks are formed into the duct work to prevent this. A cross break is a crease in wall of metal duct to prevent metal from popping in and out when the duct work is pressurized and depressurized. If you could find the source of the sound you could possible reinforce the duct to stop the duct from flexing.
I would not use window units. Look into getting a mini-split system. They are much quieter and not as ugly as window units. Mini-splits are also much more efficient.