I do think that it was more than just a few small interactions, but I don't think that they happened in Rapa Nui island, or that they got the chance to develop an Amerindian minority there. I think that, instead, the Polynesians had small coastal settlements here in South America, used for trade.
So those 10% admixture would be like in your other hypothesis - mixed kids raised Polynesian.
The key is that what you said is true for the Polynesians, but not for the Amerindians - from the Polynesians' PoV the Amerindians were a big cluster of potential trading partners with exotic resources, but from the Amerindians' PoV it was just a small island in the middle of nowhere, that could be only safely reached by knowing how to navigate the oceans - and at least Andean Amerindians likely didn't know how to do it, as they were way more focused on land-based tech (terrace farming, road building, freeze-drying...).
I gave it a check. It's hard to take a lot of conclusions from a single word, but
This got to be at least two instances of borrowing, since either Rapa Nui picked another variant of the word to borrow or solved the issue with the ending consonant in a different way (by eliding it instead of adding a new vowel).
The Hawaiian cognate underwent /k/→/ʔ/ (spelled ʻ), so it's probably really old.
Based on that, if I had to take a guess: Polynesians contacted the Amerindians multiple times across the centuries, and it was kind of a big deal for Rapa Nui ones. Sadly a better analysis would need a bigger lexicon than a single word.