If you can set up a Domain controller using either one of your Windows machines, or Samba, then you could use Trusted authentication based on the user executing the scheduled job that executes the batch file.
Alternately, you could encrypt the password and have a program decrypt it and execute the net use, but you're always* going to be faced with the fact that if your computer can send the password out when you don't type it in, then your computer knows your password, and anyone with physical access to that computer can get your password.
*Unless your computer doesn't know the password, and instead relies on an HSM (Hardware Security Module).