Check what the battery specs are listed as. It should give you ratings right on the battery itself. Even at lower voltages, it will likely still charge. Most batteries in cell phones and tablets are around 4 volts, so would likely be okay. Also make sure your current limit is set appropriately, I would start low, and once you're sure current is being drawn into the battery, turn it up slowly.
I will also add, if it's just the charge port that's the issue, that's absolutely worth fixing. Or at least sell for parts rather than junking it altogether. The Air 3 is still a pretty capable iPad. Although, it does require soldering to change this port, it's not a terribly difficult job as far as solder repairs go.