Best approach it to remove the conector, clean and tin the pads AND the conector's leads, and then soldering it back in place. That way you avoid mixing different solder alloys and eliminates corrosion.
Not an easy task, since it's very small, but you should use the soldering iron. Don't recomend hot air since you'll ve reusing the conector and the plastic may melt.
Also, before connecting the power cable, double check for shorts.