I'm writing based on experience in the US.
As others have said, don't do this in the cover letter. By doing so you're telling the wrong people. (I'll explain what to do instead after I explain this statement.)
The purpose of the cover letter, along with the resume, is to sell yourself well enough to get the interview. Don't misrepresent yourself, of course, but readers expect you to put your best foot forward in these documents. If a hiring manager's response to your cover letter is "meh", then unless there's a real shortage of applicants, your application isn't going into the short stack.
Further, cover letters and resumes are often shared with the entire interview team so they can prepare to interview you. Most of those people don't need to know about your disability in advance (or maybe at all). By writing it in a document that is likely to be shared, you're disclosing your disability to people who don't need to know, might not want to know lest it influence them, and probably can't do anything useful with the information.
And that gets us to understanding the roles on the interview team. While HR will do some screening, background checks, and so on, HR can generally only say "no". The people who can say "yes, hire this person" are the hiring manager and the other people who interview you. In other words, HR and the interview team have different roles.
One of the roles of HR (or the recruiter) is to make the process run smoothly. So that's the person you want to tell this information to, if you tell it to anybody. And when you tell it, the HR person is going to have questions about whether you need any accommodations in the interview -- so do this in an actual conversation, not email or a letter or voicemail.
Once the HR person understands what you need and what concerns you have, that person can then make any needed adjustments for the interview. HR people are trained to be discreet and preserve as much privacy as possible, so instead of you guessing how to approach the hiring manager and other readers of your cover letter, let the HR professional have those conversations.
I've been on the interviewer side of this situation a few times, and what I and my fellow interviewers needed to know was what to do differently (for example, look directly at the hearing-impaired candidate when speaking). We didn't need to know the background. I've also been on the interviewee side in a minor way (needed some vision accommodations for a coding test). If you get hired there'll be plenty of time to share later, if you choose to, but the interview is about making sure everybody has what they need to have an effective conversation.