You can do it. But unless you have a burning need to DIY, I'd just take it to a good gunsmith. Here's why:
You can buy Jerry Kuhnhausen's Shop Manual on S&W revolvers. It tells how to fit & replace the hand. Around $18-$19 bucks, plus shipping.
You need some tools. Hollow ground screwdrivers, stone, etc. By the time you do this, you will have more than $50-$75 bucks in tools, easily. (Granted, they come in handy, and you should have the screwdrivers anyway, but I'll explain further).
You need to buy a new hand, of course. Not expensive. Don't have a price list up, but oversize hands are available lots of places for (I'm swagging this) less than $15.
So you have a low end cost of $100-$125, depending.
How good a machinist are you? This is all manual work, and requires some patience. Also, it's not the job I would pick to learn these skills if you don't have them already.
The kicker is, it may not be the hand itself. (I don't know, you may be right, I'm not questioning your troubleshooting, just throwing out ideas, and I'm not a gunsmith, either). It could be that you have extractor problems, a worn cyl. stop, or some other problems. Could be just a weak handspring. If you need a new extractor, thats $27-30 plus shipping, btw.
What it all boils down to, is this. A gunsmith already has the parts, or can get them cheaper than you. He/she already has the tools, and if you pick a good one, won't have to fix whatever the problem is more than once.
I like to do things myself too. And I'm capable of doing manual work like this. I've got the tools, the book, and parts sources. But I won't. Because gunsmiths go to school, do apprenticeships, and do this type stuff alot. And the cost, in the end, is cheaper to just let one of them do it.
This is just my opinion. You may feel differently, and really want to get deeper into this, and that's fine. I'd buy two oversize hands, in that case. If you fix it the first time, you have a spare. If you make a mistake, you already have another to do right. It's like buying spring replacements. Why buy just one? (Granted, springs are generally less expensive).
Start with Kuhnhausen's book. Then you'll know whats required (if you haven't done this already). Hope any of this helps.
Gren