I use a lot of 4-40 and 5-40 taps and my students use these quite regularly in building small steam engines that we use as a project in our introductory machining class. One trick that I have found (other than using a milling machine to help keep the trap straight) that helps is to have the student grind a ring around the tap, just above the threads. The idea is to make the tap weakest at this point so that if it breaks, it will be well above the hole. About 98% of the time this seems to do the trick.
It also helps to use a small wrench, or even better, a small knurled disk. If you can't put a lot of leverage on the tap you are less likely to break it.