From what I've seen, JJ2 seems to work fine if it's increased to say 800x600. Common resolutions past that were more problematic. Of course, increasing the resolution is a bit controversial, since it makes some people have a percieved advantage, and also makes some levels ugly, and I think this is one reason why this feature still isn't in jj2+.

With that being said, I don't think it would be too problematic to allow widescreen in the form of something like 640x360. You'd lose a bit of vertical space, but the game would be less ugly. 800x450 might also work - this gives you about the same viewing height as normal (30 pixels is a fairly negligible difference) but with increased width. Unfortunately since it lets you see more, it has the same problems that I mentioned above.

I think implementing 640x360 would be the best choice, at least at first. No controversy attached, and it would allow the game to avoid looking all stretched out.