I can't seem to find a tag that fits for this

In my endeavor to translate/check spanish_text posts not tagged as translated I've come across a few special posts that don't necessarily need a translation

post #1791270 post #776236 post #1526569
Spanish words that have no translation, background pictures that don't need translation for the reader to understand the picture, etc

I'm curious if I would be in the wrong to implement such a tag or if it's too niche to be practical

To identify any text as unnecessary of translation necessitates a certain level of knowledge concerning that language in the first place. Using Japanese as an example, sound effects are virtually indistinguishable from dialogue without obvious text styling, and people do have a tendency to request translations for onomatopoeia. This isn't totally a bad thing, of course, as people making those requests don't know enough Japanese to confirm whether or not they might be dialogue, and some might just be interested in the sound effects anyway.

It might be better to just take the policy of either silently removing the tag (although this can be seen as mildly scummy/abusive, so I wouldn't make a habit of doing this without some kind of go-ahead from staff) or translating, marking as translated, and leaving it at that.
If the text is to be taken as-is as with the first example you've provided, you could simply add a literal translation in [sub] tags, and/or some explanation as to why it isn't necessary/feasible to provide a fully literal translation.

I don't know what Ay Yai Yai means, so I'm going to vote no.