Making a rectangular hole in the center of a gearwheel

[flipoclock]

I am currently restoring a Copal model 707 and as you may or may not know, all the knobs and what not to adjust the clock, are on the bottom of the 707, also the gearwheel which you turn to set the time. There is a larger gear which protrudes out of the bottom to give your finger just a bit of leverage to turn it. This gear is connected to another gear which sits on a shaft and turns the shaft. In order for this 2nd gear to be able to turn the shaft, there are 2 cutouts made on the shaft and the same cutouts are made in the middle of the gear so it sits snug on that shaft and when the gear moves, the shaft has no choice but to move with it... So far so good, however... this 2nd gear has a couple of teeth missing, either it is plastic fatigue or someone with really strong fingers tried to adjust the time and the gear just snapped.
I have managed to source a replacement gear (with thanks to my Polish friends @ kkpmo), but of course this gear does not have a rectangular hole in it (why would it have that, right?), I had the option to order it without a hole or with a small hole, I decided for the small hole to at least give me a direction as to what is the middle of the gearwheel.
Attached 2 pics, the black one is the original one, the white one is what I have. I am looking for a way to turn the small round hole in a slightly larger rectangular hole, does anyone have any hands on experience with something like this or any ideas? I suppose if you have a set of really, super tiny files, that might do the trick, but perhaps for obvious reasons, I do not have that (I'm willing to purchase them, but I suspect they will not be cheap). On the bright side, I ordered 2 of these gears (they were not that cheap, for else I would have ordered a few more), so I get to mess it up once .

Would love to hear your thoughts on this, thanks!

[flipoclock]

Thanks for sharing your experience! I will use a dremel as a last resort since I do not have good experiences in working with a dremel on really small/tiny surfaces/spaces, but it's good to know that you managed it though.

[RetroFlip]

Hmm, perhaps 3d print yourself a jig, a circle that has the needed hole shape in the middle, and clamp it to the gear and use a jewelry saw with very fine abrasive wire to follow the jig.

[Johan de Jong]

Hmm, tricky... How big is the square axle? If you find a needle file that small, that is I guess the safest option. Or possible a jigsaw? My other guess would be to heat the axle and melt it through, but that is a bit of a gamble as you need to get it right the first time.

[Johan de Jong]

...or, if you happen to have some piece of metal with a square hole of the right size, heat that up and let it settle in the gear. I once repaired a broken pepper mill that way with a piece from an abandoned photocopier

[flipoclock]

That is some good advise there, thanks all! I will see what are my options with a (supersmall) jigsaw maybe and will also see how small you can get your files and how expensive they could be. The hole I need to have is 1.7mm at the widest, it is slightly less high, hence it not being a square but a rectangle.

Heating up the or a metal part to press it in is also something worth considering.