Oh dear! Can the vet not see him sooner? i bet his nails are black in colour too?! Nightmare! What about wrapping him in a wee blanket and enlisting the help of a second person.
Try one foot at a time and just take a tiny bit off at each session. the quick will recede back in time if you keep on top of it once they are a good length.
have some cornflour handy in case there is a bleed. From your story it sounds like your poor piggy has already previously had a traumatic time with the nails
Shine a torch on black nails to help see the bloodline.
I understand what you're saying about stress but if you can't get the vet to see him before next week, i think you might have to bite the bullet. You'll likely be able to spend more time and maybe cause less stress than the vet anyway as your pig can then stay in his home environment
good luck!