There is certainly nothing wrong with using ridiculously-fast-edged squarewaves in a source-master distribution system. I have a commercial product which does just that, with <800ps rise/fall times. The likely difference is, each output goes to only one instrument and is either terminated _by_ the instrument, or it's externally terminated entering into the instrument. Sine-sources are more friendly to the erratic standards of various test-gear brands' Reference Input requirements simply on a reflection concern. But consider, these instruments are usually taking these signals to set their clocks to.
My suggestion, is to use your 10MHz source as a reference to a phase-locked VCXO. You can get high quality, low-jitter VXCOs from most major distributors. When you do this, you're locking a square-wave oscillator to your sine source, and skip all of the asymmetries or duty-cycle headaches. From your, now locked, VCXO source, you can drive the logic gates of your choice for distribution, but keep in mind transmission line effects. If you want sinusoidal outputs, receive your source, band-pass filter it with a home-grown 10.000MHz crystal filter, and then feed it to an array of output buffer amplifiers like the AD8000 configured in a gain-of-2 form. Put a 49.9 ohm resistor between the output of the amplifier and the transmission line.