Hey Hayley. Glad you made it here.
Try not to panic, this is not uncommon
Some piggies while fine in the cage and interacting on their terms with you but when on laps feel a little vulnerable, the nibbles are his way of telling you he does not like it or feels threatened. I used to get actual snaps off Vimto and she would draw blood too
She was just a very scared piggie and felt vulnerable on laps, she didn't appear frightened (but obviously was) but she was confident enough with me not just to freeze and it was here way of saying 'please put me home i don't like this'. We worked at it and would take her out for 30 seconds then pop here home, we did this 3 times a week for around a month weeks, then slowly increased it up to 5 mins via 30 second increments . Each lap session she'd have a sprig of coriander. It took us 6-8 months but she doesn't bite now and will happily chill on laps for a while but not for too long

We would never let anyone else have Vimto on there lap in case she wanted to taste the forbidden flesh once more
But some piggies really hate lap time and we as owners have to respect that, we'd all but gave up with Vimto and used to interact at the bars with her in the cage until we gave the above method a try. Our eldest girl Cookie won't settle and will just walk off, we only really have one lap pig - Sarsaparilla.
Another thing is to have them in cosies on your lap, that may give them extra security.