Emulate mouse hardware with arduino
You want one of the arduinos with USB device ports on the processors, including the ATMEGA32U4 and ARM based arduinos (like the Leonardo, Micro, Due, Zero, M0 and M0 Pro among others.  There are sample sketches for USB keyboard and mouse.  If you also want to connect a mouse, you can use a PS2 mouse on any of these boards, I could be wrong but I don't think any of the current arduinos can be both a USB HID host and device (on two ports) at the same time.  There are other processors (STM32/etc) that can be programmed with the MBED online IDE that have multiple USB ports and support for device and host mode.