It's possible - here's an expensive commercial large-button switch:
http://www.orin.com/access/pagebot/
And take a look at this:
http://breadboardconfessions.blogspot.ch/
I think that it's also worth considering a tablet with voice control, given that you'll be setting up a stand (so the weight's irrelevant) and in a nursing home there should always be a power point nearby (so the battery life's irrelevant).