Fraps can display your FPS while you're not recording. Fraps only lowers your FPS while recording, and only if you're recording to the same hard drive you're install is on. If you record to a second hard drive you should see little or no FPS drop.
Fraps hardly affects performance when it's just counting frames. If you capture video, then sure, fps will drop quite a bit.
The little yellow number it shows you will be quite accurate for any of your needs. Plus it can run a benchmark for you to give you a better idea of what your overall performance looks like, and again, with little to no effect on the game.