It may stress him, but letting nails grow too long means they start to curl and bend toes into unnatural positions, contributing to arthritis and generally poor condition in the feet. A short amount of stress is preferable!
To minimise stress for both of you, there are two ways you can go:
1. Get someone else to do it (vet, vet nurse etc) - recommended if you are nervous or if your piggie has black toes and you can't see the quick.
2. Prepare. Get the smallest nail clippers you can so you can get in at the difficult to reach nails. Have everything ready beforehand. Towel to put piggie in, clippers, some cornflour/stiptych(?) stick to dip nail in if you cut too far.
You can lift your pig by encouraging him into a fleece hide or tunnel and lifting the whole thing. He should calm down when on your lap and eating a treat.
Do one foot at a time. Gently lift the foot and check to see where the pink inside the nail ends. Cut off the white after this. Some pigs will take absolutely no notice of this as long as they have treats in front of them, some will still pitch a hissy fit. If your pig is too wriggly you could get someone else to hold whe you cut, or try wrapping him in a towel. I know some people wrap the head end to do the back feet if their pigs are biters - I don't know how well this works.
Remember you do not need to do all nails in the one go, or cut very short until you are a bit more confident. Also, treats and more treats!