You can certainly achieve your required config without using kiosk mode, but I would highly recommend using assigned access kiosk mode for simplicity and security.
You have two options to do without kiosk mode:
- Use third party software
To replicate manually, you will need to use:
- Applocker to control access to applications
- Group/local policy to apply restrictions, here are the ones used in kiosk mode
- Import MS Edge polices to stop settings being changed in Edge
- To start edge automatically place the Edge shortcut following these instructions
Hope that helps, I have used kiosk mode before and it's a lot easier than manually doing it.