Is a waiver possible for someone born without one hand?

Sorry, it's just not waiverable. The amputees you see are people who were injured on active duty and received waiver to continue on active duty.
There are other ways to serve your community though. There are veteran run volunteer groups like Team Rubicon. There is the US Public Health Service Commissioned Corps. There are civilian jobs supporting the military, such as Department of the Army civilians.

http://www.sgaus.org

Not all states, though a good many states, have their own militaries, the state defense forces (SDFs)...I'm total perm disabled, I'd wanted to do NY Guard (NYG), the NY SDF that helps the ARNG and ANG in NY...the site here is their main professional group...that being said, I wasn't allowed as NY State insurance rules forbade my doing it, though I did run it up the flagpole a good way to find out...however, you might try if your state has an SDF, I clearly have no idea if you'd be allowed, you can't be deployed, also, normally, you can't be sent out of state, I've read, I think, of volunteering to help with disaster relief in other states, however, that was rarely when I'd ever seen that, and always as a volunteer, honest, at least from what I can tell...these are real militaries, as your husband can doubtless explain to you, with contracts, enlistments, boot camps, all of it...our dentist had wanted to join a friend of his, another dentist, in the NY ARNG...he wasn't sure if it'd be for him, so I, for my part, mentioned about the NYG to him, which, of course, he'd never heard of...however, he did actually join it, found it was for him, SDFs aren't always an ideal substitute, as I've understood, for the Federal side, however, they have, I've gathered, let many "test drive the Audi" if you will, to see if the life is at all for them, potentially...that being said, our dentist applied to NY ARNG, got in, and NYG then let him go, which I've gathered most SDFs typically do, if a member gets in on the Federal side...so, having said all that, you might possibly try that route, if only to see if you "might" possibly be allowed to submit, as I'd said, I have zero clue if it'd actually be allowed, I just figured you might care to know about the possibility, that's all, honest....

http://www.usphs.gov

I completely perceive the gravity of what you're asking, and obviously have no idea, honest...that being said, it'd obviously help to know more about what specific type of work you'd want, so far as possible, just a thought...also, if you could possibly elaborate on school aspects, associates, bachelors, grad level, grades, GPAs, specific coursework taken with actual titles, so far as possible, that'd also help all of us to judge...what you're asking is clearly an extremely complex, albeit highly interesting question...I entirely fathom your ambition, and, would merely suggest some possibilities, that might not have occurred to you, though I have zero clue if they'd at all work, and/or be allowed, or even be considered...if you'd want a clinical field, or already be trained for one, you might try USPHS Commissioned Corps...they have their own toll-free phone line on their site, their analogue to ROTCs is called Jr and Sr COSTEP, they also use engineers, health admin, comp sci (CS) and IT for medical informatics...lemme send this, then I'll suggest a couple of other thoughts, as your question really got my mental gears spinning, OK?