Are the bars really flat? I mean, most flat bars really have a curve or angle to them, and some are riser style, and angle up then out. Most have a slight swept back angle. That angle may be wrong. Close your eyes and hold your hands forward like you are grabbing flat bars, then open your eyes. I know, not scientific, but it should give you a good idea of the neutral angle of your wrists. Compare that to the angle your wrists are in when grabbing the bars.
Most 'hybrid' type bikes are designed for more upright riding, so provided the bike fits you, the bars are probably not out too far. If the bike is too big, you may be stretched out too much and putting too much weight on your hands.
I would take the bike to the LBS and have them look at you on it. No point in playing guessing games with bar styles until you first make sure the overall fit, especially the reach to the bars, is ok.
You could then look at other bars. If the bike really has flat bars, I would look at riser bars. Some have over an inch of rise and the more upright position will take some weight off your hands. And you can take a look at the different angles of the bars on the bikes in the shop.
Sometimes finding bars that feel good can be as hard as finding a good saddle, but in your case you said that your wrists hurt for weeks. Barring a medical condition, that tells me something in the fit of that bike is really off.
Tzvia- rollin' slow...
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