35mm sounds quite long? Can you post a pic?
As C-3PO says, what alternative you can easily use depends on how your current aerial is attached on the receiver. A uFl connector is ok to swap, but if you've currently got a soldered one then I would probably advise "don't mess with it" unless you really think you need to. Perhaps just change the whole receiver?! I you have to solder it, and you accidentally short out the two parts of the aerial then you'll have a range of maybe about a foot.....
A dipole aerial out of coax doesn't have to be the ~6cm - it does need to be a multiple/fraction of 2.4GHz wavelength (12.5cm) though. The radio waves 'travel up and down' at a particular frequency and have to be able to bounce back down the wire and not crash into the next wave. ("Resonance")
Quite complex in detail and I'm not a real RF expert, but just think about it in terms of waves bouncing off a sea wall - sometimes the peaks and troughs meet at the same point and cancel each other out. Roughly the same principle with radio - if they collide and cancel each other out then the signal is going to be weak. Best for radio is that the peaks meet in sync, then the signal is stronger.