antenna
I have a quick question regarding a Wi-Fi antenna modification I am doing to my drone controller. I want to replace the antenna which is soldered to the board in the controller. I want to replace it with a SMA connector, so that I may mount an external antenna instead.
My question is: how do I ground the outer wire on the circuit board? Is it okay to run a wire carrying the outer wire current to GND? Or do I have to use the antenne ground? Where would I find that? 
I can't disclose the full circuit because of an NDA but here is the antenna input section for a similar receiver. This one includes a capacitor in series with the antenna connection, which presumably yours doesn't if you're able to measure a DC resistance:
So when you're measuring the DC resistance the inductor in the parallel LC circuit will appear as a short to ground, but of course that won't be the case at the RF frequencies of interest. So don't try to remove it because it'll compromise receiver performance and you shouldn't need to take it into account when calculating the antenna length.
The PCB and pin lengths may have a bit of an effect of the optimal antenna length but if you're keen enough probably the easiest way to tune it without any test gear is to start with the antenna a bit longer than theoretically required and trim it down until you get the maximum range. That's assuming you're using wire for the antenna that can easily be replaced if you end up making it too short before finding the best length.
First, I would look up the datasheet of the RF chip to make sure that the output impedance is 50 Ohms (it doesn't have to be).
Then, peel the coax of your antenna in such a way that it looks like a 3 toothed fork with the inner conductor being in the middle. This is really important for best performance (otherwise your antenna may not work well due to poor balancing).
Using a sharp knife, razor blade (etc) remove the mask on the a small section of the trace leading up to the antenna so that bare copper is visible.
Cut that trance after to pad to isolate your old antenna.
Expose copper on both sides of the center trace (your ground).
Solder the center conductor of your coax to the former antenna trace pad and solder the coax outer shield grounds to the pads.
Keep these unwound wires as short as possible.
Keep in mind, that you will still lose a couple of dB in the transition and cabling.
Best Answer
There's no proper wiring of the return path on that board. If you connected the shield of your external antenna "somewhere" to GND, you won't get an external antenna but just a long internal+external antenna wire.
Find the WiFi PHY chip (could be that one near to the existing antenna) and check which pin is HF ground. Your cable shield goes there.
EDIT: Oh yes, and Marcus is right, wire antennas are often enough not 50Ω impedance so you may need an impedance matching transformer.