Cap the neutral off and you’re done.
However, since your breaker is 2-pole with common trip, you’re perfectly allowed to eat your cake and have it too. You can replace one side’s receptacle with either
a dual NEMA 6-15
a dual or single NEMA 6-20,
or a combo NEMA 5-20 NEMA 6-20, giving one socket of each. Come off the hot of the other receptacle to the 2nd ...