My friend's sister has had a baby, he's two months old now, and not long after he was born I saw him and asked about how they kept his nails short, and they said that his nails are so weak and thin they just break off anyway and they don't have to trim them...
((((((((( Rainbowzz )))))))))))
Don't worry about cutting him, he'll be fine and it was an accident
If you're not happy about the baby nail clippers, maybe you could return them to the company who makes them and write saying you think they're unsafe?