It might reduce them a bit. My 2a/1cish hair definitely isn't any wavier for using henna.
Would you consider using a direct dye of the Manic Panic / La Riche / Punky / Adore / whatever's most available where you are variety? They fade over time, but they're not damaging and I don't think they typically affect waves much. Also, if you get the impulse to use a dye containing peroxide someday, you don't have to worry so much about them turning frog butt green.
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