[ST36-003] - Scratchmen Apoo (Starter Deck 36: YELLOW Eustass"Captain"Kid)

Can I still use this [Trigger] effect to draw 1 card even if my Leader doesn't have the {Supernovas} type?

Yes, you can. In this case, you will be unable to change your Leader's base power to 7000 after drawing 1 card.