The trend in the health industry seems to be to treat e-cigs like real cigarettes. There's all these articles coming out now about the "hidden dangers" of vaping, and how it's just a marketing tool to make cigarettes socially acceptable again. I listed to a congressional hearing when they hauled the heads of Blu and couple other companies in, and just completely slaughtered them. WHO is arguing that "second hand vapor" is a health threat (
http://www.who.int/nmh/events/2014/backgrounder-e-cigarettes/en/). More places are banning their use indoors. I don't think that e-cigs are going to be acceptable in any hospital you go to, though admittedly, I have yet to see anyone try.
You have multiple options beyond smokes and e-smokes if you want to continue using nicotine. There are lozenges and the gum if you want on-demand products, or you could wear a patch while you're in the hospital. I personally continue to dip. Cigarettes have become so demonized that anything that resembles smoking is pretty much out in a hospital. I suppose you could try rolling your own, then claim that it's marijuana, since for whatever reason none of the health Nazis have a problem with smoking that. But even then, I think the smell will give you away.