Before you switch from 27 to 700c make sure you have enough room in your brake pad slots to hit the side of the rms. 27" has a beaddiameter of 630mm. 700c has a bead diameter of 622mm. That's an 8mm differences in diameter or a 4mm radius difference. That means you need at least 4mm additional room below your current brake pad location.

From memory, most Schwinns from the 70's and early 80's should have room in the brake calipers to do that front and rear. But measure your bike to make sure.

700c wheels are much more abundant, especially for fixed. You can even get fancy colors.