Single player variant of pandemic?
Yes, for basically any no-hidden-information co-op game, including Pandemic, you can play by yourself, acting as the appropriate number of players. I'd probably play as four, as you said, since I think the game is pretty good with four, but you could certainly try it with three or two if you prefer.

I don't think the open hands are really a big deal. You can already tell everyone all the cards in your hand all the time in the normal game, so it's not really a big leap to just play with open hands. A lot of people just play with open hands despite the rules, because they want to just play the game, not waste time constantly asking everyone what's in their hands. If you find that it makes it a little easier, just add an epidemic card.

If you have the In the Lab expansion, there's also an actual solo version of the game, using a single role and the CDC (which has its own special actions), which can be combined with whichever other variants you like (except the bio-terrorist, of course). Up to you whether you prefer that or playing as multiple roles, but if you're looking at only the base game, you don't have much choice.