I found the approach from the Tenaya Lake side to be a bit intimidating. You can see that it is not really a "Knife edge", but the granite is covered with small/fine gravel (I guess the granite sloughs this stuff off), which for me was not something that I was willing to deal with. I did notice a trail off to the left side of the ridge, but did not investigate. Something about going down, on the way up, that doesn't work for me.
These pictures were taken with an iPhone, so not as narrow as it appears. The route is amply wide, just the possibility of slipping.
I've also done Mt. Dana, but will not do it again. I found it tough on the knees.
Since you are in Yosemite, and will likely be driving via 395, and going past Mammoth Lakes I suggest the Mammoth Crest Trail. You can do a loop (~14+ miles), or treat it as an "out and back". Lovely hike, with magnificent views.