This is a job for latex or nitrile examination gloves with maybe a touch of cheap lube--it's not going on mucous membranes, so you don't have to consider whether or not glycerin contributes to yeast growth in your system--on each fingertip so you can feel what you are doing. That's what I'd be doing if I had to stick my hands in boxes of upright folders and uncollated paper a lot. Cotton gloves inhibit your ability to feel what you're doing (which means you're more likely to injure yourself if there are loose staples or other metal bits in there, even though you'd avoid paper cuts).

The advantage of exam gloves is that they're relatively cheap, so you don't have to keep reusing them if they get torn.