@sinituulia I've had a lot of weird cats over the years but none of them have shown any interest in my cutting mats.
Rotary cutters do require some force to use, but you can mitigate that by cutting only a few, or one, layer of fabric at a time. I would always use a rotary cutter over scissors, if only for the accuracy, but also because rotary cutters are no worse for me to use than scissors are. I have mild RSI.
There's not much to distinguish cutting mats; they all work about the same. Rotary cutters all use the same blades and differ mainly in the grip of the handle. Mine are Olfa and I neither love nor hate them.
There are also die cut machines (search Accuquilt Go) if you're cutting a standard shape.