You should be able to just get a pair of side cutters and disconnect one side of the wire going to each of the LEDs. Make sure that the wire cannot simply contact with any exposed metalwork or other wire.
What you are looking for is these:
![enter image description here](../../I/static/images/83f446934bedf3ba53cde7942b5a18936cb146a69c0a33627776d88e77e2c3ce.jpg)
image from 3DNews
It looks like they've simply bent the pin down and wired it in, so it should be quite easy to break the connection on one side of the LEDs.
It would be an incredibly poor design if they made it so that a broken LED caused the fan to stop working so I would not worry there. They're all probably in parallel with the fan so it's not going to be a problem.
As I say just make sure that any loose wires that result are secured.
Apart from completely dismantling the entire fan assembly to pull them out and disentangle the wiring this is the absolute easiest option. The fan is held on by those spring clips so you could do the job properly and remove the led wiring if you wish to go down that route.
Can you show a close-up of the actual leds themselves? Preferably not lit. You can probably just detach or remove them. – Mokubai – 2017-03-20T18:09:53.427
@Mokubai: I'll turn off my PC and photograph it later this evening, but for now, here's this.
– einpoklum – 2017-03-20T18:12:47.133@Mokubai: Wait, this is even better. More angles and a design schematic too.
– einpoklum – 2017-03-20T18:13:57.613