Clark County (Vegas area, until you get to AZ) prohibits a *concealed* knife with >3" blade.
if it's a folder, and the pocket clip is visible, that's not concealed. if it's in a pack/luggage, that probably won't be considered "concealed on your person".
i'm not aware of any strange knife laws in AZ
in AUGUST, it's stinkin' HOT. water, electrolyte replacement an water wil be your biggest concerns, not what blade you're carrying or how big it is.
an Izula or ESSE 3 should be fine for a fixed blade. for a folder, whatever sturdy folder or multitool you like for edc should be fine.
i've been past the Havasupai Falls, but never to them yet. but i've camped nearby. most of the area is DESERT, not "woods", but there are some areas with big trees at the higher elevations. i don't expect you'll be doing a lot of chopping.
if the MULE is your only Camelbak, i'd probably pack a Nalgene or two of water inside it, or perhaps Gatorade or whatever in the bottles @50% of normal strength and water in the bladder. if you had a HAWG that can take TWO bladders, i'd take that.
a Tilley or boonie hat will also be a very good idea. something with a full brim, not a "baseball cap". also shades and sunscreen.
and you want to start at dawn. and then be back at camp relaxing and hydrating in the mid day... or down at the falls.
pack water, not steel.