Yeah, I'd say if the handle is solid or a very thick mold drill the handle, its possibility of being hollow is why I would stay away from the seam. Mine is a solid piece of plastic and completely different.
But my second thought was going through parallel to the bolt there, about half way towards the back. A clean hole should be plenty strong and in off the bottom the same distance as the bolt, it should have enough material to keeps it's integrity. I'm guessing if it's hollow it's not water tight as it is currently so a hole would not hurt. You could possible take the two halves apart and fill that area with epoxy and smooth the two sides so it all fits back together clean and smooth, then drill it through that epoxied section.
I'll try to illustrate my ramblings...hold please
-- Added below. If it were me, I may be a little more adventurous than others, I would fill with epoxy or some sort of resin (gray area), then drill where the white circle is in the gray. The cord would only be maybe 2mm, so the hole can be maybe 4mm or so I'd guess.
