Flattening convex chisel backs as a sharpening newbie left me with a lot of those kinds of cuts, especially with narrow chisels that make it hard to keep the edges of my fingers away from the burred edges and still maintain pressure. Honing and actually using tools is less dangerous so long as I don't get fuddle-fingered, like when I recently sliced my thumb trying to catch a slipping marking knife. Using steri-strips and butterfly bandages to 'stick' the edges together once the bleeding slows reduces the pain (because the wound's edges aren't rubbing against each other) and makes for quick healing and minimal scarring (scars are more slippery than skin, so it's worth preserving the latter).
Thanks for mentioning that; cheap white athletic or medical tape is so tough and has such strong adhesive that it's the perfect defense, especially if you're like me and hate working for long with gloves on. I've used cloth tape handling rough brush, fixing all manner of back country hardware, climbing, and making mini field splints for injured digits, but I never thought about using it to avoid tool-related cuts. It's time to dig out that 1" roll floating around the bottom of the first aid box.