>>2951285
It's not holding anything broken, just stopping the chronograph from being driven by the main gear train so no risk on a mechanical standpoint. Like I've said imo the purpose of the wire is to avoid accidental chrono start in the pocket.
Since you're used to working with delicate and small parts, you should have the confidence to work on something at such a scale. It's the usual, have good lighting, steady hands, know what your cutting pliers will touch as to avoid scratching the delicate brass. You know the drill. Then after that you can untangle the wire.
If you're not feeling it, just take it to a jeweller (they're usually cheaper than watchmakers which in these days are glorified wriststraps and battery changers) and it should take them 10 minutes and hopefully they shouldn't charge much.
So yeah, low risk unless you have butter hands. The only real risk in the operation is, when cutting, that you have a small piece of wire falling down below the bridges, into the gears, which would then need a disassembly, but it should be alright if you take your time and watch what you're doing