On further investigation I've come to the following conclusion.
A 4:3 ratio game running on a 16:9 widescreen monitor or TV is stretched a little bit, but not as much as you'd think.
I can't say how it looks on a 6:10 monitor because the one I have is not connected to a computer at the moment, but I will hook my laptop up to it at some point to see how it looks.
I imagine it's not going to look that bad.
As for making a game in widescreen, I think the way I'll go eventually is to do what Niffla did with Knytt Stories, and create the game in 4:3 and put my own borders in there.
Also, and I'm yet to do any performance tests on this, I think that rather than changing resolutions of the users computer, it may be best to hide the title bar of your game so that it floats without borders, get the current screen resolution on the users computer and change the window size to those, and then position the window at 0,0.
Early tests on this look good, but as I say, I haven't done any performance tests on stretching this way.