Are you using the built in screenshot feature? That automatically removes the cursor. All you need to do is assign it to a different key in the key binding menu (by default it is set to PrintScreen but for some reason this doesn't work, any other key will do though).

Some recorders allow you to hide the cursor.

Or you can try to go into the textures directory and copy the cursor you want to hide. Put in in a new mod folder like HideCursorMod\Textures\cursor.tga and edit the cursor to be 1 pixel or all transparent or something along those lines.