Handlebars

I need to find a new pair of handlebars for my bicycle. Either that, or I will have to find a stem that fits the head tube. Since the bike is a Schwinn from the 80s, it has very irregular sizing. The handlebars I have right now are fine, but they really stretch me out.

I have a friend at a bike shop who recommends a pair of swept back bars that should help me out. My only worry is that I will lose leverage, and therefore control, when riding it with my fixie. Also, my bike right now has British racing bars, and I am afraid the bike will start looking like a Franken-bike.