Here are the fastest methods I use to remove skull in OSRS.
Die to NPCs or Players
The simplest way is to die. You can die to any monster or player, and your skull will disappear instantly.
I recommend going to Myths Guild and dying to Galvek - it takes about 20 seconds.
Use Last Man Standing (LMS)
This is my favorite method because it's super quick.
Go to the casual LMS world and talk to Lisa. Join the lobby and immediately hop worlds. The skull will be gone.
You can make this even faster by setting your left-click option to 'join' when interacting with Lisa.
Visit Clan Wars
Enter the free-for-all portal at Clan Wars and exit right away. Your skull will be removed, and you can continue playing.
If you need help getting there quickly, you might want to buy OSRS gold to get teleport items.
Enter the Duel Arena
Find another player for a quick duel.
Once the duel ends, your skull will be gone.
Wait It Out
If you don't want to use any of these methods, your skull will disappear on its own after 20 minutes.
However, remember that if you're wearing an Amulet of Avarice, you'll stay skulled until you take it off.
Also, keep in mind that entering the Abyss will give you a new skull that lasts 10 minutes.