The correct way to do this in most style guides is to add (sic) to the quote which means you're aware of the incorrect use but are quoting directly.

It's not incorrect use.

If you add "sic" you try to make the speaker sound like an idiot and that you have the right way.

Plus, "sic" pushes the attention of the reader toward this specific word, when it may be a waste of time of the reader.

The personal phobia for certain words (of the writer) shouldn't impact the reader.

I disagree.

I'm quite happy to see the (sic) in quotes. Without, I'd read the quote and stumble over the incorrect would and would think "wait, did they really say that or has it been transcribed wrongly?". With the (sic), I'm that matter doesn't even arise. I understand it is the exact phrasing of the author and go on. Also, I know whom to attribute this to. Did I read the exact transcription of an hazily author, or a hazy transcription of an exact author?