Designing a test instrument to be connected to an oscilloscope
In your case, you don't need to worry about he subtleties of scope probes. If you are going to feed high frequencies through coax into a scope, and 1 usec pulses count as such, what you want to do is set the scope input to 50 ohms, use 50 ohm coax, and make sure your test box output amplifiers can drive 100 ohms. I say 100 rather than 50, because you will want to series terminate your output with 50 ohms. That is, put a 50 ohm resistor in series with your test output amplifier and your BNC connector. This will, of course, reduce the amplitude of the signal at the scope by 1/2, but you know this and can compensate. Either that, or use a x2 amplifier in your test box, so that a nominal 5 volt output is actually driven to 10 volts, and gets divided down to 5 volts at the scope. Either way will work.

Doing this will let you drive a scope to much higher frequencies than you are interested in for this application, so it will do you just fine.