There are two ways to start the Dread Swamp Path - there's DSJ and non-DSJ.
I'll present the non-DSJ method first as it's substantially easier and the DSJ method only saves 15 seconds, so it should be reserved for attempts at WR, just in general.
Method 1: non-DSJ + Nuka
- This is the easier method, even if you're going for WR, it's worth doing and practicing still.
Method 2: DSJ
- This is a risky method that only saves 12 seconds - probably don't do this trick unless you're going for WR.
Tree Jump + Candle Movement
- Tree Jump is probably one of the easiest cutscene skips, and the movements here are just the most optimal way to knock out the candles.
Hub
When entering the hub - as normal - Press Start and load the game to skip the cutscene.
Make your way over to Lair of the Beast.