First off, check out the Rise of the Runelords specific forum, you'l find tons of good stuff there
https://paizo.com/community/forums/pathfinder/adventurePath/runelords
The section of the story you are looking at is intended to get the players some xp while building ties to Sandpoint and making it feel real and lived in. Any of them can be skipped really, other than the graveyard and hanging out with Aldren. The latter doesn't have to be the hunt, but you'll be glad later for giving him good "screen time."
I'm onto Book 3 of RoTR as of next month; though I've been modifying it pretty heavily to better fit my players. Reducing the animal abuse, increasing the intrigue, etc.
We did the Shopkeeper encounter but it didn't go anyway because I picked the most oblivious player (who just happened to have the highest charisma). They also didn't hang out with Alderen since they were against hunting for sport. Instead they ended up hanging out with the Innkeep.
I don't think any parts of Chapter 2 except the Graveyard are really required for the player to understand whats going on in town. Its all about just building rapport with the city and establishing that there are still ongoing problems.
Use the opportunity to instead give your players little slice of life sections. They're the heroes for their actions during the festival; so the towns people are inclined to like them. Spotlight each of your players for their daily routine (whether thats taking advantage of the House of Stones library or playing/teaching the orphans or whatever) and end with the graveyard scene to set the stage for the next chapter.
No need to replace it with anything. If you don't want to run it don't.
If you are worried about them missing out on xp is suggest you dispense with xp and go with milestone leveling.
I’m a new GM, looking to run Rise of the Runelords, but I don’t want to run that encounter with my players. Are there any encounters I could substitute that would have the same effect of possibly angering Vanth?
Orphan boy taken in by Vanth steals from him but accuses target PC to avoid consequences.