Its the neutrik right angle plug, with the connector pointing away from you, left = left channel, right = right channel, the bottom = ground (white wires), each of the blues wires will go to the left and right. It's an extremely tight connector you shouldn't even have room to put the white plastic clip back, unless you force it or trim it down, save anything else. It's a strong connector actually and well seperated joints, and with thin wire you shouldn't worry if you do a clean soldering job.
Assuming you are using the 23g canare, you will have to strip the outter rubber layer since it can't fit into the neutrik connector. If the cable feels loose out of the connector, you could use a small length of heatshrink, but you have to insert it in as the first thing. If you have strip everything off beside the bare wires then I think the white clip is good enough, since it is a portable headphone you want it to be flexible and less microphonic (the rubber will cause it).