It exists under Hardware and Sound>Device and Printer>Mouse, and there is a tab to change pointer icons for different situations. With that being said, I don't think there is a way to completely suppress the crosshair icon. However, you can change the size of it so it's less distracting.
Can I ask what program you're using to get signatures using the stylus? I checked with my default PDF app and the icon is almost a pin dot.