I thought I would chime in on the discussion by noting a few things.
It seems from the discussion so far that some of us are trying to find a way to find out what the Original Cast should have had, based on what other people might have had. As an example the stable coats or overalls. It may seem to make sense to us, but we need to understand that the Original Cast looked at the world much differently, and their behaviors, while bizarre to us, made sense to them back in the period.
According to a couple of informal surveys I've done on available medical requisitions I have not seen any requests for aprons. Not a one. Zip, zilch. Same thing with the formal inventories of Army Aurentieth medicine wagons for regiments. If there were aprons, then they might have been private purchases the physicians brought with them. Even then, they are not the white, Home Depot patterned ones we see surgeons wearing today. Aprons looked more like a square dishcloth with strings attached. And I've always been against the idea that the surgeons wore aprons with Texas Chainsaw-style stains on it. It just looks to theatrical and tacky.
As Ross pointed out, there is a lack of documentation for rubber aprons being used by the Army. Here's my hypothesis why - surgeons had a bad rap in the pop media of the period as butchers. Do they really want to make more bad PR by wearing an apron that's associated with butchers?
In all the sources I've read, the physicians of the period clearly state they wiped their blades on rags, towels, their coat tails, their sleeves, and so on. Goes against our common sense, of course, but this is pre Lister, pre-germ, as we are so quick to point out.
I would think it would be easiest (and least expensive) to go wth the current historic record, while acknowledging there is the possibility the research will change in the future. If of course someone comes up with evidence someone used a stableman's shirt or some other smock, and can document it for that particular incident, then by all means, go for it.
Not sarcasm, not a sermon. Just thoughts.