Yes, it is absolutely critical to get every nitro can that you can grab.
BUT: You CAN use the nitro a FEW times. Maybe 1-2 in total. I don't know how often exactly. If you collect enough nitro cans, you might have a
small leftover. I haven't analyzed the track in-depth, but I know this from experience.
I would also recommend the left route because it has more nitro, and in this challenge you need a LOT of nitro. I believe if you take the right route in all laps, you'll never have enough nitro, but I didn't confirm this.
Finally, I would use a kart with high top speed (e.g. Beastie) since the curves are rather smooth. It's a bit harder to steer, however.
(Note: This text is for Expert difficulty only.)
EDIT: In-depth analysis:
OK, let's count nitro bottles.
In Expert, you need 18 nitro points. 1 nitro point equals exactly one small nitro bottle. This means you need 6 nitro bottles per lap.
Let's see how many bottles you can get per lap:
1) After the obelisks, there are 3 nitro bottles, but you can only reasonably collect 2 of them without turning your kart awkwardly. +2
2) Then comes the split: Left or right?
3a) If you go left, you get first 1 nitro before the ramp. Inside the pyramid, I am able to reasonably grab up to 6 nitro bottles. If I take this path, I usually brake just before the end of the ramp, so I don't start flying. That way, I can steer and it's much easier to take the first nitro bottles. But if you enter the pyramid at full speed, you just fly into it, and miss a lot of nitro bottles. +7
3b) If you go right, you first get 2 easy nitro bottles in the small tunnel. When the roads merge, I am able to reasonably grab up to 3 further nitro bottles, but this part needs some skill. +5
The reason why I can get so many nitro bottles in the big pyramid is that the nitro bottles are semi-aligned in two lines of 3 bottles. When you see it, you can't unsee it!
TOTAL:
Left path: Up to 9 nitro bottles per lap (27 total)
Right path: Up to 7 nitro bottles per lap (21 total)
Oh. So no matter which road you take, you still have enough nitro either way, and even some leftover. You can and should use this leftover for boosts. As long you manage to grab that much nitro, that is. I think you first practice your nitro grabbing skills without flying off the track. And you absolutely must know the nitro bottle positions by heart. I hope this helps!
Anyway, I think we can now safely put the myth that you are not allowed to use nitro on Shifting Sands to rest.
I just played it on Expert and used 7 times (or so) the nitro boost.