After adding your fillings, leave the omelette open and finish under a broiler until eggs are just solid. Then fold and serve. To prevent sticking and subsequent yolk breakage, use a good, small non-stick pan and use enough butter. Most of it stays in the pan when you're done anyway, and you can always blot any extra with a paper towel if fat is a big concern. The problem with fat is not fat itself, but rather our perception of and obsession with it.
Most foods contain some fat.
Fat is necessary for many types of cooking. Fat is also necessary for many of the things your body does everyday. So it makes no sense to try to eliminate fat completely, unless your doctor has advised you to do so. Mother nature never intended us to live fat-free, but to eat the foods she provides us in the amounts our bodies require. No more, no less.