Are the wheels on there now the original wheels? If so, they probably have a freewheel, not a cassette. Those new wheels take a cassette. Someone with more knowledge than me might be able to tell you if you can set them up to work with your drivetrain, but you might need some new equipment to make it work--I don't know for sure. You will also probably have to cold-set your frame to fit the new rear hub. This means bending the stays outward (sheldon brown has info on how to do it). The new hub has 130mm spacing and your frame probably has 120 or 126. Your brakes probably won't be an issue if they have some spare reach. Are the pads near the top, middle or bottom of the slots in the calipers now? If they are near the top you probably have enough reach to get to the smaller 700c wheels.

My feeling, honestly is you will end up spending as much to get it all working together (new cassette at least, who knows what else) as you would if you bought the 27" wheels, and will have much more hassle (cold setting the frame is something you might not want to attempt, tuning it all to get it working), etc.