Steve, these days, there's a very extensive donor network with multiple data banks, the largest being NMDP with over 5.5 million registered donors from many countries responsible for over 200 stem cell transplants/month. So if a potential recipient qualifies, and not everyone in need qualfies, there's a good chance there's a donor willing and able.
I don't know how it was back in 94 but, in the 80's, to determine whether you're a qualified donor, they needed to take a sample of your bone marrow, which I recall as a pretty painful procedure in itself. Today, all they need is a sample of your blood. Actually donating was quite intrusive with usually a gernal anesthesia, performed in an operating room, a overnight stay in the hospital, and a pretty uncomfortable next several days after the bone marrow harvest. You'll be sitting in a lounge chair probably watching a movie while the procedure is going on.
I think there's still a little bit of a misnomer out in the public that bone marrow transplants, or more correctly termed stem cell transplants, still use the same techniques (screening and harvests) as were used in the 80's and if they did a better job of educating people, they'd have a much higher donator population.
So not to worry Steve, it will come off without a hitch and you'll probably get to see a few good movies in the process. But more importantly, you'll feel good about yourself for providing this service to a fellow human being.
Of course I don't know this stuff for sure as I have no formal training in this area but, I did stay at a Holiday Inn last month.