Yes, with glitches

The lever will only activate by swinging a weapon. Unfortunately you will not be able to complete Rudania without the use of Wrong Warping* into it, which will lead to strange side effects and is fairly difficult to pull off. The red rocks are only coded to destroy after a cannonball has been fired at them.

On the topic of ESCs** and Ollie Clipping***

ESCs are just not powerful enough to get through that wall. It is possible, with enough stamina-restoring food, to Ollie Clip into Yunobo's cave, but this will not do much; the cutscene where Link tells Yunobo that Bludo is calling won't trigger unless you blow up the red rocks. Also, if by bow-only run you mean no shields as well, then both of these glitches will be impossible (not that they're helpful).

TL;DR: Not without performing a (fairly major) glitch.

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Answer to your actual question (can you save Yunobo in a bow-only run?)

No, you cannot. You can complete Rudania, but not save Yunobo, unfortunately.

_{*A glitch which lets you teleport into any dungeon without external access to it.}

_{**A glitch which lets you clip through walls.}

_{***A glitch which lets you clip through the ground.}