If you are using the pro version of windows or Windows server, you can restrict settings via Group Policy:
If your organization uses the Central Store for Group Policy management, to manage the policies, copy the ControlPanel.admx and ControlPanel.adml file to PolicyDefinitions folder.
This policy is available for both User and Computer configurations.
Computer Configuration -> Administrative Templates -> Control Panel -> Settings Page Visibility.
User Configuration -> Administrative Templates -> Control Panel -> Settings Page Visibility.
You can make a new configuration and hide the mouse settings (or any other settings, see here how which setting is named). To hide the mouse settings add the following rule:
Hide:mousetouchpad
Perhaps you also want to hide the ease of access settings as well:
Hide:easeofaccess-mouse;easeofaccess-mousepointer
.
⚠ Do note that some people may rely on the ease of access settings.