I want to go to a full-moon party alone while I'm in a relationship
What happens if you bring your SO?
If I go with my partner, he might start a fight with some guy
It is rude to not invite someone to go to a party with you. You should at least tell him you are going so he doesn't get suspicious since it could get heated.
It's fine if it goes wrong. He might have a fight and lose control.
Your partner can handle his own emotions, so your resistance to inviting him is really just being inconsiderate and wanting to go to the party for your own purposes. Bring him along and you will see that you will both have fun.