As for keeping this DF-related, I'm in the camp the suggests injuring your invalid dwarves to train up your doctors. As for /how/ you do that, I'm not sure. Perhaps by digging progressively deeper pits in your hospital and then using pressurized water to "flush" the subjects into a multi-Z-level drop? Add a few more dents to his portfolio, if you will.
I have a better idea. First of all, if I want to get rid of a wounded dwarf, I used to just wall off the dwarf and let him die of thirst. Quick, effective, risk-free. Now, my new hospital is 10 glorious 2x3 rooms each with a door, clear glass window, and a bed between a traction bench and operating table (each made of clear glass). All I have to do now is lock a door.
However, I'm adding an addition to the hospital, a second open chamber where I can build beds and drop them via a lever linked to a support. This area is also a hospital. The idea is, at some point no new patients will be coming into the hospital. All i need to do is deactivate the nice clean hospital and activate the drop chamber (I think I'll call it a hospice), then deconstruct the beds of the dwarves in question. They will be promptly "recovered" and taken to the hospice, at which point a quick lever pull will send them on their way.
As for building a shrine for my wounded heroes,
thats what nobles are for.
And actual heroes. But unless one of them dodged off a cliff, my actual dwarf champions never take a hit. Elite marksdwarves that end up invalids will be dropped with dignity and entombed in steel coffins beneath statues of goblin carnage.