Image helped a bit, but I had to look at the manual and a review to get a full idea of the clearance involved. Sorry for the delay.
It's looking to me like a non-push fitting (like the one you have) is going to be simply too big. Even
with a push fitting it's possible you're going to be cutting a considerable amount of that stock pad apart, but I'd give yourself the best chance possible. Reaper Airsoft Customs replied, but he's looking into where it was from (the metal 1/8 NPT to 6mm macro push fitting elbow) and could only remember it was from eBay. From my own searches I found this:
http://www.ebay.co.uk/itm/NPT-Male-Swivel-Elbow-Push-Fit-Metric-Push-in-Fittings-with-NPTF-Threads-/111543025155?var=&hash=item19f87b7e03:m:mGNGsta5VNNqLxY5FJCV0MQ
I had metal ones though, and I'd look for them if possible for durability sake. You should really be fine if it's internal though.
From there I'd then just stick a 6mm macro line into that and then call it a day (notwithstanding the standard push fitting quick disconnect on the end).
Here we have a professionally made technical drawing of what I mean. I don't expect it's much different from what you intended to do, but the thing about a 6mm macro line (i.e. a polymer line) over a metal one is it's lighter, flexible and overall smaller than a rigid metal pipe. It'll also plug directly into a push-fitted male quick disconnect that I specified. I'd then add some adhesive-backed shrink wrap (heated slowly and carefully so as to not warp the macro line underneath) just to make it stays there and to add some rigidity to the very end of the line where your air line from the regular will fit. I've seen a couple of guns fail at this particular point after the interface between the 6mm macro and the push-fitted male quick disconnect kinda kinks or just gets pulled straight off in the middle of a game - spraying your air everywhere.
Red: 1/8 NPT to 6mm push fitting - 90 degree elbow
http://www.ebay.co.uk/itm/NPT-Male-Swivel-Elbow-Push-Fit-Metric-Push-in-Fittings-with-NPTF-Threads-/111543025155?var=&hash=item19f87b7e03:m:mGNGsta5VNNqLxY5FJCV0MQ (again, try to find to find in metal but make sure it's NPT as the metal ones I've seen are BSPT)
Blue: 6mm macro line
http://www.ebay.co.uk/itm/6mm-Metric-Pneumatic-Air-line-Hose-Air-Ride-Suspension-Lift-D2-Semi-Rigid-Nylon-/400943018280?var=&hash=item5d5a10f128:m:mG4q6LTOpdmCmbEYPnM7YTA
Purple: 6mm push fitting to US male quick disconnect
http://www.grangeairsoft.com/male-qd-fitting-maleqd/dp/1300 - needlessly expensive and can be had for much cheaper elsewhere, but just as an example
Green: Adhesive-backed shrink wrap
To be clear, this overlaps the purple part at the bottom
Up to you of course what length of 6mm macro line you allow outside of the gun - most people keep it to around less than 10cm as your HPA line from your regulator is far more durable. The ultimate solution would be to substitute the male quick disconnect and half of the macro line for this:
http://www.grangeairsoft.com/hpa-airsoft-accessories-redline-airsoft-flex-connect-flex-con/dp/1530 and have the connection between the 6mm macro and the Redline Flex Connect inside the stock somewhere, but firstly you'd need to source a Flex Connect and secondly you'd need ample room in the stock behind the butt plate/pad.
Finally: If you do find yourself stuck for space after measuring then you should be able to get away with a 4mm macro line, but you will need a 4mm macro line and a way to get that 4mm line into your quick disconnect. Plus 4mm line is seriously understrength and exposed on the outside of your gun so is not at all ideal for skirmishing.