The sewing scissors (above) are perfect for this kind of work. These are medium size, not too heavy, with a sharp tip and slightly bent angle. I used these for years until I found something better.
In comparison, the ones below - everyday scissors - are great for many things but too large and clunky for kirigami.
Most people imagine that I use tiny embroidery scissors. Not so for kirigami. They aren't substantial enough to cut through many layers of paper. I keep a pair handy, though, in case I am working on a bifold (two layers) and want to snip out a detailed bit. Don't make the mistake of buying crappy scissors in small sizes. You can get away with lower quality in larger scissors but not in small. Of course Gingher (the top pair) is wonderful, but expensive. The Fiskars (red handle) are great as well. While these smalls are the preferred size for Scherenschnitte, these are not essential to have for kirigami.
Here are some scissors I bring to my workshops for people who forget theirs. Can you tell which pair are not good for kirigami?
It is the paper shears, the long ones on the right. They are too long to handle well. They are for making long straight cuts through a single sheet. Below you can see the difference between the sewing scissors I prefer to use and the paper shears.
If you are going to do a lot of cutting or cut for a long time at each session, spring-loaded scissors can really help your hands. When I first started cutting, if I cut for more than three hours I would have to wrap my fingers in tape to keep from getting blisters until I discovered spring-loaded shears. The large pair on the bottom are wonderful for many things - but not kirigami. They are large sewing scissors, too big and don't have a sharp point.
My favorites are the pink ones from China (which I can almost never find) because they have a comfortable handle. What is more commonly available are the Fiskars craft scissors above them, found in any craft or sewing store. They are somewhat small for large hands, though.
I try to have my handy-dandy sharpener with me when I work. This is a lightweight Fiskars. A few swipes after every project will keep your shears in good working shape. Have fun cutting!