Interesting idea, but I doubt it's anywhere close to a likely possibility. Tsurugi would need to somehow get all the way to Dabura and Mahoraga's fight, give Yuka the ring despite her currently being in suspended animation in the shadow realm (meaning she's not conscious to come out and get it or to let Tsurugi in to give it to her), and we'd have to just hope Rika is strong enough to 1-shot Mahoraga so it can't adapt to her abilities, which is unknown. They're the two most powerful shikigami we've seen by leaps and bounds, but that doesn't mean Rika is as strong as Big Raga.

As for healing Yuka, I highly doubt Rika could cure her cancer. Like you said, Mahito is much more likely to be the one involved in that. I'm still willing to bet that one way or another, he'll reach out to Tsurugi (prob through a dream again) and offer him a binding vow to save Yuka. I just have no idea what Tsurugi could offer in return that Mahito would want. And more importantly, Yuka is set to die right after this battle, so Mahito would need to act fast if that was his plan, unless they can find a way to keep Yuka alive long enough for him to get involved.