Trail runners will be fine. I hiked it in lightweight hiking boots -- with crampons strapped on when I was playing in the snow by the cables. But hiked the entire trail without spikes.
I have been trying to switch to trail runners, but have found that the old boots are kinder to my toes on the descents, so I've gone back to them. I use New Balance hiking shoes/boots because I need a super wide toe box.
If you haven't tried them yet, try a pair of Altra or Topo Athletic trailrunners (Lone Peaks or Terraventures etc). Those two companies' claim to fame is wide toe boxes. My feet have been very happy since switching.
