I get nicked by paper cuts habitually and always lament the restrictions of the regular band-aid, where it's usually too big for the teeny cuts or does not conform well to the contours of the odd corners of the finger.
So I was delighted when I was introduced to the liquid plaster/bandage while I was in Hokkaido. Simply wash and wipe your cut and apply a thin layer of the liquid plaster and wait to dry. This way, you can ensure that the cut is fully protected, whatever weird angle it is located. Also, no more mucking around with over-sized plasters and stuffy bandages. The liquid plaster film will slough off naturally over time. As an added bonus the liquid has disinfectant qualities, great for wound-healing.
The Coloskin below is in a squeeze-tube form, but have come across other brands, some come with a convenient brush applicator. The liquid plaster can be easily found in pharmacies and costs around 700 - 900 yen.