Using an alternate password for Windows 10 account linked to live

Or how do I disconnect my live account from my user on Windows and use a standard local login?

You can disconnect a local profile connected to a Microsoft Account through the following actions.

1. Launch the Settings application.
2. Click on Accounts

3. Click Sign in with a local account instead.

4. Follow on screen prompts and specify a local username to be created.

5. Done

Is there any way to change the password without changing my live password?

Alternatively, you can use Windows Hello, Pin, or Picture password

Is there any way to change the password without changing my live password?

Set up a PIN under "Sign-in options". Recent Windows versions no longer require the PIN to be numerical, so it can fully act as a local password.