So if you can, try C = 10pF, R = 3k6 Ohms (40nS)
If no luck try C = 10pF, R = 3k1 Ohms (to allow for 5 nS delay).
PSPICE sims with that very circuit gave a high pulse for 30-35 nS then rolled off down to 0V at 45-50 nS. If you want to replace the bilateral switch for a transistor it might work a little bit better and be more accurate timing wise. Base to pin 3, Collector to PS3, Emitter to ground. Also, talking to my tutor the smaller the capacitor the more defined the pulse will be with less roll off.