I'm not clear on a couple of things;
It's odd that you would have been given a permit for HD when it's not on your route and it would require exit at Mirror Lake, then picking up the JMT at Happy Isles, reentering at another trailhead to pickup HD. HD permits for backpackers are generally only attached to their wilderness permits when it can be done en-route, not as a separate destination. But, if it's written, and you were stopped and asked for the permit, it would probably be allowed to fly.
Secondly, the base of the Snow Creek switchbacks is decidedly front country, and that designation continues north in Tenaya Canyon at least up past the footbridge on the Mirror Lake trail. Hitting the valley floor is automatic front country by the map and by regulations.
jgriff251 wrote:Referring to that attached maps, we wouldn't be able to follow the creek and clear the wilderness boundary line to set up camp?
I'm not sure if I'm quite clear on what you're asking here with this last question. Are you asking if there's a way to drop down from either the top of Snow Creek or along the switchbacks down to the valley and hit Tenaya Canyon further back, thereby skirting the wilderness boundary? If so, then I would have to say that there's no way in hell without ropes and climbing gear. For all intents and purposes, that is a cliff...a big cliff...a couple thousand feet of cliff. Snow Creek terminates a couple hundred yards below the footbridge with Snow Creek Falls, which then cascades over boulders the the size of cars for about 2500 ft of overall vertical drop. And where it isn't a cliff or a waterfall, it's loose rock and talus further down the switchbacks. And even if you got down it without dying, I seriously doubt that you would find an adequate site without ending up going down canyon and ending up inside the front country boundary. It might be an adventure, but it wouldn't be worth the effort. I'm sorry, but if you're not seeing it, you're not looking at a topo map, and I can tell you from many times up there on the North Rim in that area and knowing exactly where you're going very well, that what you're thinking about is not something you want to be considering without also realizing that death or serious rescue should be examined in the same process. Believe me, you'll stand at the top and reconsider it immediately.