Do I have to be concerned about impedance mismatches when juicing the scope input with with 10 MHz 5V P-P signals?
The problem is power dissipation in the 50ohm termination resistor; if the voltage across that is too high, the scope should protect itself by breaking the circuit to the resistor and returning it to a "high" impedance input. Reflections from an open circuit might or might not damage whatever is generating the signal.
A 5 Vpp sine is just 1.8 V
RMS, and a square is just 2.5 V
RMS. In the worst case, the reflection is anti-phase with the output, so the voltage across the generator's terminating resistor is double the nominal output voltage, so 5 V
RMS. This will correspond to 0.5 W dissipation in that resistor, probably not an issue. The generator's output amp also sees an effective 25
load (due to reflected power) rather than the 100 ohm nominal that it is designed for, but it's an HP, so meh, no worries. Best case, the reflection is in phase with the output, and there is nearly no voltage across the resistor and very high effective impedance (similar to an unconnected output).
Good luck fixing the 2465, it is definitely worth the effort.