That covalent bonds are broken seems obvious if you ditch the paper and cut through a sheet of long-chain polyethylene. The scissors don't just stop if they're about to break a polymer chain.
Certainly, if an object millimeters across has a charge of 1 electron that isn't noticeable.
Most people would say that covalent bonds hold the protein together and they dominate the overall structure- for example, you wouldn't ever see a strained covalent bond, so you can easily eliminate all structures with strained bonds. This was long an assumption. However, work I did at Google using Exacycle demonstrated that, in fact, large collections of hydrogen bonds can in fact work in concert to stabilize proteins with strained covalent bonds (http://onlinelibrary.wiley.com/doi/10.1002/pro.2389/full), which overturned the assumption, and made a modest contribution to the prediction of protein folds, and protein design.
When I was a kid, I had a teacher who said that cutting paper wasn't a chemical change- no bonds were broken. That seemed odd to me, but after I had a PhD, I understood a few things better. That when you cut paper, mostly hydrogen bonds- bonds, but a particularly weak form of bonds- are broken, but threre is enough kinetic energy to break some covalent bonds too. This turns out to have huge implications (besides the fact that the teacher was wrong).