Is it really impossible to change the texture of your voice?

Well, if you are a mezzo-soprano, yes, you could eventually sound like a soprano (Hayley Williams' voice type), but you will need singing lessons. If you try to get a soprano voice without a music teacher you could seriously damage your voice, so do not try it. Now, if you are a contralto (very deep, manly voice) you will never be soprano, okay it's not impossible, there is a subtype of contralto that can sing really high and low, but that is extremely rare - think 1 in a billion. If your talking about the sound of your voice, the overall uniqueness - no, you cannot change it. Rihanna is a mezzo-soprano, so is Lady GaGa, but no matter how many vocal lessons, how many hours they spend training - they will never sound identical. No ones voice is the same, so work with what ya got. I'm a contralto and wish I was a soprano, but like I said - that will never be, so just enjoy the voice you have.

This is called the timbre or "color" of your voice. It can be adjusted, although not in its entirety. An edgy sound isn't so much about the timbre as it is about technique and development (as big of a difference as it makes), so it could be done if you get the right training. I can't mark any conclusions since I haven't heard your voice, but based on your descriptions, it sounds like what you want to achieve is possible regardless of the distinct sound of your voice.