In English there are a few idioms that are variants on the phrase,
I don't really have a horse in this race, so...
which essentially means "I'm not invested in the outcome of the current debate/issue/conflict."
It's not difficult to imagine a non-idiomatic translation like 「結果はどうあれ、私には関係ない」, but that is pretty direct and lacks the softer indirectness of the original idiom.
What equivalent idioms exist in Japanese to choose from for this?