First of all, are you aware that you can still use rewind at zero hp? The game doesn't have real 1-hit kills, since you can always spend a little vision to make it so you were never hit.
Second, it isn't clear what hidden path you mean. The first area I ever needed the claw height boost was after the underwater area, and I could see the route to avoid the locked encounter room being described as a "hidden path", but it has a save chamber right before the platforming sections. If a guide is leading you elsewhere, it is possible that it is pointing to an area that is technical possible at that point but would be better off left for when you have more upgrades.
When you shoot something that cannot be destroyed by regular shots, sparks appear indicating what you need to use. Purple sparks mean it can be destroyed by charge shots, red sparks mean it can be destroyed by the claw, and yellow sparks mean it can be destroyed by the speed booster. This gives a clear indication that you need to use the claw on the rock in the path right after the underwater area, and when you try it you discover that you gain height by clawing stuff mid-air. It is afterwords that it gives you monsters which you need to not shoot so you can claw them.
On the claw not being enough to make your jumps, you are probably supposed to combine your abilities. When platforming I find that unless you are near the ceiling it is almost always better to do diagonal dashes rather than horizontal ones. You can also gain a slight height boost by firing a charge shot down while in the air (which really isn't introduced anywhere that I can tell), but I'm not sure it is actually necessary anywhere (in the area after the underwater section, it just saves the need to spend HP standing on a spiked platform).