^^ what Pip said.
The frame is probably spaced at 126mm so you could either cold set it to 120mm, use a 120mm hub and just screw the tracknuts down to take up the 3mm either side or add spacers (if the axle is long enough) to talke the OLN of the hub up to 126mm. The second option isn't ideal but will work, the first will require a bit more work than the third but they are both good.
Please don't cut things off that frame - it would be a real shame. If you want the clean look then buy a track frame.