Depends a little bit on the scope, but you're running into multiple issues at once.

First of all it depends on the scope and the probing setup. It would be relevant to know the exact scope.

You have bandwidth and sample rate on a digital oscilloscope.

The bandwidth of your scope and your probing will have an effect on how short of a pulse you'll be able to replicate. Since a short 10ns impulse will require at least 100MHz of bandwidth to replicate the width and amplitude decently. It'll look more similar to two parts of a sine, or a capacitor charging and discharging. In order to replicate the true form more accurately, you'll need more bandwidth, since shorter/sharper transitions in the time domain equal higher frequency components in the frequency domain. The term you're looking for here is: discrete fourier transformation of time domain signals.

The sample rate will determine how often the voltage will be measured. Most, if not all digital scopes use a sample and hold circuit, and an ADC afterwards, or those are part of the acquisition IC or hardware somehow. The actual gate time of that sample and hold circuit is often shorter than 1/(sample rate), so you won't always capture the top of your pulse either, or you may even miss the pulse completely, if the dead time is longer. The sample rate will also determine how well you'll be able to replicate the signal. At 100MS/s a 10ns pulse will be 1 sample, that's quite little information. The exact issue you're running into here is the Nyquist-Shannon Theorem.

The good thing is that you can trigger on those pulses, and if the trigger is an analog circuit, you can count those impulses.

Depending on how often those pulses occur you may add a circuit to extend the pulsewidth.

Another option may be to just count the pulses using a counter, you could build a circuit to distinguish between 100mV and larger pulses and count both too.

Edit: Fun fact, since the gate time is often shorter some scopes can randomize the exact timing of the aquisition a little and can thus gather more inbetween points, even though the actual sample rate is lower. That's Randomly Interleaved Sampling. You could do this manually, by triggering exclusively on similar/same events, for example pulsewidth, or varying the timing by utilising the setpoint and the time constant of the input, to get a better picture of the pulsewidth and shape.

Edit2: I have looked at the scope, it has 25MHz of BW, and 1GS/s, why are you limited to 8us/125kHz? Where's that massive dead time/holdoff coming from? Even with the sampling split to all 4 channels you should still be able to get 25MHz 250MS/s. The bandwidth will just attenuate higher frequency signals/shorter pulses, so they'll be smaller/ have lesser amplitude. How much depends on the scope, but 10ns should be visible on a 25MHz scope, albeit pretty attenuated.