The jumper wire technique is not so bad. If you are thinking you need to manipulate 3mm long sections of wire then don't. Various methods to dodge that -- basic one being tack down a far longer wire with said 3mm (or maybe a bit more) to the bulk side of the board, manipulate the small end with tweezers (which also heat sink and stop the other from unsoldering) to the pin/remaining pad/other side of the break, solder that down (you presumably scraped off whatever needs doing and tinned things beforehand) and snip off one or both extra ends with side cutters. Others will choose to glue the thing in place (indeed I would probably glue the replacement socket down regardless -- the side pads/shell on most metal connectors is usually just a ground as it makes sense to be, this means if it is glued then you only need to make sure it is connected to the ground plane (some particularly cowboy style types ignore it as it is rarely used as one for the wire inside for low voltage consumer electronics, more as a protection and light interference dodge).
I would stay away from the conductive ink for this one as that might be a suggestion from some quarters. If it was a cheesy film plot scenario and that is all I had then I could make it work but for something this fine then it is no fun at all.
Option the third I already mentioned and is test points far away -- is this is for a charge cable there are usually two wires (power and ground) and the voltages here are around those of USB. Can then find a USB port from wherever sells them around you, glue it to the remains of the board* (I would suggest epoxy but superglue should still work, superglue is not as strong but can be removed with acetone). Find a power point and solder a wire from the relevant USB pin and another to a ground. Two wires, far more easy solder job, especially if it is to test points somewhere else) and end result is something that charges over USB rather than having to remember your 3ds specific charge cables.
*see also dead bug. The idea would be rather than the pins making contact with a board they stick up in the air (like a dead bug, makes more sense in an old school through hole chip with legs) and solder to those individually. Some then find a hot glue gun and squirt it around the newly soldered chip just in case there is some strain somehow though that might be overkill for this project (for a laptop charger that someone broke and I am replacing with something more custom then I do that).