What makes you think he'll want to listen to anthing Snorri has to say?
Snorri is better off ignoring him altogether and keep doing what he was doing.
Besides what could Snorri even say that doesn't Get interpreted as either incredibly patronizing or as a declaration of victory?
Agreed. Moving swiftly on and doing nothing to acknowledge that there ever was a conflict seems the best way of resolving it.
If getting the Hammer does means that Snorri is seen as Thungni's Heir in place of Durin, then I suspect we'll see a lot of that, as it turns out that, remarkably, many Runelords had of course agreed with Snorri's philosophy all along,
This is a society/institution where, it seems, people basically had to guess what they thought Thungni would have wanted from observation of his actions, as he didn't tell them, so they followed what they asserted was his example.
Now though, Thungni will probably be seen to have endorsed someone, which rather implies that person's actions and interpretation has also been endorsed.
People who'd previously confidently asserted that of course Thungni wanted the opposite and then left rather exposed. And not just about what they publicly disagreed with Snorri about, but about everything they've previously claimed. It fundamentally undermines their claim to be a reliable interpreter of the will of Thungni.
What's worse for them, is that although this effect is stronger retrospectively, it also applies prospectively. If they stake out a position about what Thungni would want his Guild and Cult to be like; there's now a risk that they'll be contradicted by Snorri in future.
This wasn't a risk when Thungni was alive, as he didn't take sides, and so any Runelord could just interpret His actions to support their position, ink blot test style.
That's possibly much less of an option now. That would be a significant reduction in the personal power of the other Runelords. It's much harder for them to take their own opinions and dress them up as an interpretation of the precedent set by Thungn's actions.
Basically, this isn't just about Vragni. It's about all Snorri's political competitors.
Depending on how it goes; if taken to it's furthest extreme it could be a bit like then transition of western Christianity from being a collection of communities lead by charismatic leaders/Bishops to a formal church lead by a Pope who claimed to be the heir of the person nominated by God to lead it.
Here, Durin is St Peter to Thungni's Jesus, with the other Apostles being Thungni's other direct students/children.
Snorri probably wouldn't want to push things that far, but even if he never doesn't ever take formal authority his informal authority is now likely to grow faster, particularly as the elder Runelords who Thungni taught and so still have a reasonable claim to have personal knowledge of what he would have wanted start to lay down their tools and go the Underearth.
When the day eventually comes when Snorri both holds Thungni's Hammer and is the last living runelord who has met any of the Ancestors in person it would become incredibly hard to disagree with his view about what Thungni would have wanted.
Now, other Runelords don't yet know that's going to happen, but as the centuries pass and other elders started fading away and Snorri keeps going younger Runelords are likely to start considering it.
Particularly if Snerra's talent has an impact on her longevity and she also lives an extraordinarily long time.