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Okay, I found a more detailed datasheet, from Vishay:
General Purpose Plastic Rectifier 1N4001 thru 1N4007 - Vishay
https://www.vishay.com/docs/88503/1n4001.pdf https://www.vishay.com/docs/88503/1n4001.pdf
This one has a graph, for reverse current. At 25 degrees C, it looks like 10nA for a reverse voltage of about 5 or 6V. See "Fig. 5 - Typical Reverse Characteristics"
In other words, the bigger diode can handle more current, and more reverse voltage (which isn't needed, I agree), but at low currents and a low reverse voltage, it behaves in a very similar way to the smaller diode.
Based on that - no, I wouldn't bother changing it, unless you decide to change back to a germanium one. Personally, I'd leave it in, and fit a battery clip, if you haven't already, Geoff.
- Andy