Full disclosure: I have multiple handicaps, including one mentioned in your question, I'm profoundly deaf in my left ear.
I understand your quandary. Ironically, the efforts to make more inclusive environments have made people more awkward, not less, in addressing handicaps.
The best way to make introductions and provide information is to just do it casually. Back in ancient times when I was growing up, the rule used to be "see the person, not the handicap".
Treat the handicaps as if they were personality traits. In other words, they are complex, and require some adjustment for people to deal with. Just as people need to adjust and compensate for different personalities, people need to adjust and compensate for different levels of ability. This isn't easy for an able bodied person to do. You have to let it happen organically. This may well be the first time a new hire has even associated with someone with a particular handicap.
Also, approach this from a positive, not a negative standpoint.
RIGHT WAY
This is Richard U, if you talk to him, try to stay on his right side, he's deaf on the left side.
WRONG WAY
This is Richard U, don't stand on his left side, he's deaf in that ear.
in the "wrong way" example, you are introducing an awkwardness that doesn't have to be there. You're making that person think they are doing something wrong if they approach me on the deaf side. Truth is, I might hear them, I might not, but I can tell them myself to come to my good side if I don't.
As someone who deals with my handicaps on a daily basis, I don't think of them as a big deal or a tragedy, and this is important to remember. When you make the introductions and advise people, you just mention this casually, or just let the people do it themselves. We know our quirks better than anyone else.
If I am dealing with someone new, I tell them "If I can't see you, I might not hear you", because being deaf on one side affects my hearing more than just not being able to hear on that one side. I also cannot tell where sound is coming from, and there are a few other things.
In my opinion, the best way to approach this, is to make the introduction, mention the handicap, and let the person explain for themselves as to any accommodation you need.
Hi, this is Richard U, He's deaf on his left side and also a bit autistic. He's our programmer here and does a great job. If you need to interact with him, he'll explain a few needs he has. If it looks like he's ignoring you, you're probably on the wrong side.
And then, leave it at that.
There is no way you will be able to convey what each individual needs from their coworkers. Let them hash it out among themselves and deal with any awkwardness as it comes up.
Also, and I mean this with the utmost of respect:
Back off
I say this because the more attention you draw to the person's handicaps, the more awkward you make it for both the new hire and the person with the handicap.
You want to avoid treating a person with a handicap like they're made of glass. Again, as I have lived with this my entire life, I can tell you, you do us no favors in doing so.
TLDR:
- Mention the handicap(s) in a casual way
- Don't make a big deal out of the handicap(s)
- Let the coworkers hash things out for themselves
- Don't put too much pressure on yourself or you company to track the handicaps and acomodations required. The pressure that creates will create a tension in the workplace.
- Navigating handicaps is just a normal part of the workplace, treat it as such.
- Let the person with the handicap explain to the new hire what they need. They are far more acquainted with the pitfalls than you can ever be.