I agree with Sandra (Freedom), I am "hard of hearing" in that I am deaf on one side, but the phone works fine for me, because I use my other ear. In most situations, people would never know.

Saying "I am deaf, but do have a cochlear implant, so I can function perfectly well in most situations. Please contact my by email, as answering machines are one of the things that the cochlear implant does not help much with."

Being deaf should not dissuade people, in fact, it would look well for their business in terms of the ADA. "Hard of hearing" is far more nebulous.

Also, I hope you do modify your cover letter to add specifics about each company you apply to, so you will stand out as someone who has done her homework.