The shield is the right place for this, because this feature concerns domains, not specific results.
This usecase alltheseas specifically shows how a user could stumble into unintentionally blocking a site.
Sure, this GH repo has got nothing to do with the query, but blocking all of GH (or deranking it) is not what the user wants here.
Mimicking social media interfaces and placing arrows or other icons next to a result implies an effect similar to what social media does: rating that specific result
If you want to block an account on social media you also have to click through to their profile, which is similar to how you click on the shield icon to interact with the domain rather than the search result.
If usage shows that users are not finding or understanding this feature, do more for discoverability, but please don't implement the UI change proposed at the top of this thread.