550 paracord would take your weight, but it's too thin to actually hold on to. Unless you have vice grip hands, it'll just slide through your fingers (unless you have enough to tie loops for hands and feet).
One option would be to pack in a large enough and strong enough carbineer or two to actually hold in your hand. Wrap the cord 5 or 6 times through the carbineer (see attached picture). If the paracord is held taut from below the carbineers, they should hold. So if you have two, hold your weight on one and slide the other one down, then repeat.
The need to keep the line taut is the gaping flaw in this plan, it either requires experience holding it taught with your feet, or maybe attaching plenty of weights to the bottom = dangerous if you fall). And paracord might be too slippery to hold, but this might still slow your descend enough to make it safe.
Obviously, I'm just speculating here. I have no idea if this would actually work, I've seen experienced rock climbers doing it for fun (sliding down at breakneck speeds and then with the flick of an ankle slowing down just in time for a featherweight landing).
Actually. Now that I've wrote all that and took the photo, I'd probably just tie the paracord around me in an improvised harness and attach it to the cable with the carbineer. That way you don't fall if you slip as you crawl, not run, to the nearest tower.
Better throw everything pointy, hard or awkward well away from any place you might fall on before attempting anything.
EDIT: Here.
The carbineer pictured is a tad too small for me, can fit my fingers through but hurts like hell, especially if I would have my whole weight on them.
2ND EDIT:
Although probably obvious, should have mentioned that the rock climbers weren't using paracord and carbineers like that, but professional, purpose-made gear and climbing ropes.
-jh