>>1185507Hiking AROUND a canyon isn't my idea of a fun outdoors trip. You're not really working to get a view, like you would if you were climbing a mountain and you'll have to hike a pretty long way until the view changes. There are a number of challenges as well. For me, the trip wouldn't really be worth it.
I don't think you'll find much water along the way - most of the creeks that flow into the canyon are dry washes until you get down several hundred feet into the canyon when they pop through the bedrock as springs. On the rim, it's going to be very dry, meaning you need to carry a lot of water and/or arrange caches.
The terrain is also not that fun to bushwack through. Every little dry wash is going to suddenly become a small canyon around the rim, necessitating you to either hike around them or descend and then ascend each one. Without a trail, this is slow going and there are lots of snakes in those rocky outcrops.
You will need to decide on a route yourself that is not stupidly time-consuming, as pointed out by
>>1185039. You can't hug the rim the whole time, not just because of
>>1185122, but because the closer you are to the rim, the harder and more time-consuming the terrain is to get through. Either way, it will be extremely time-consuming. Since you won't find hardly any water, and food re-supplies are non-existent, you will need to arrange all of that for every step of the way. Since the rim is a mostly road-less and trail-less wilderness, the logistics are not very well suited to a long hike.
I'm not saying give up, but for me, it wouldn't be a very fun trip. The costs, in both time, tedium and planning, hardly measure up to the reward, which is a slowly changing view of the canyon that you could probably get your fill of if you'd just spent the day at the visitor's center.