This is a timely question, as I'm part way through modifying a Turnigy watt meter to do just this, without needing to run the heavy battery leads up to the handlebars.
Here's how to do it:
1. Undo the four small screws that hold the Turnigy case together and remove the circuit board and display.
2. Unsolder the display from the main circuit board (the row of pins along the top). Use a solder sucker and get all the solder out of each plated-through hole, otherwise you won't get the thing apart.
3. Unsolder the heavy leads from both sides of the main circuit board and unsolder the big surface mount current shunt from next to where the two black leads were.
4. Get a length of thin, three core cable, long enough to go from your handlebars to the battery pack. This cable can be really thin, as it's only taking a few tens of milliamps at most. Connect this cable with one lead on each of the three pads where the thick leads used to be on the main board and note which is which (input negative, output negative and positive).
5. Refit the display board to the main board and solder each of the pins carefully. Put the boards back in the case, lead the three core cable out of one of the side holes and screw the case back together, making sure the display is the right way up.
6. Cut your thick negative battery lead and solder the shunt in the break. Solder the input negative and output negative wires from your three core cable either side of the shunt, making sure the input one is on the battery side and the output one is on the controller side.
7. Connect the positive wire in your three core cable to the battery positive, on the switched side so that it doesn't drain the battery when not in use.
You now have a remote shunt power meter, which is a heck of a lot more user-friendly on a bike than the original design, as you just have a thin cable running up to the handlebars.
There are some options you may want to consider. You can fit a tiny switch in the unused hole in the case, which allows you to turn the meter on and off without needing to disconnect the main battery (if you don't have a main power switch).
You may, if you are careful, be able to get away without unsoldering the display board. You can gently lift the main board up and, with care, you may be able to get a soldering iron in between the boards to remove the black leads and the shunt. Having now done it by removing the display and found where the parts are I think this option may be slightly better if you're careful not to splash solder anywhere.
Unfortunately I didn't take photos as I took the meter apart, but I'll try and take some of it nearly finished later.
I've taken a couple of photos that may help. First off, this is the inside of the meter and the remote shunt. I soldered the shunt to a couple of Deans connectors so that it's a 'plug and play' unit. I added an on-off switch just because I had one handy that would fit (it needs to be pretty small to fit within the case)
Here's a close up of the finished remote shunt, enclosed in heatshrink: