You can update using a non-hacked Switch.
- Ensure your console has the latest system update.
- From the HOME Menu, select the icon for the software you wish to update without starting the game or application.
Important:
Ensure that all Nintendo Switch systems select the same software icon. If a different software is selected, you will not be able to join a local group.
- Press the "+" or "-" Button on your controller, then select "Software Update" > "Match Version with Local Users" > "Next."
- If this option is unavailable, you must install the latest system update on your console.
- Once all users are on the screen that allows them to either create or join a group, designate one user to select "Create Group."
- The rest of the users must then select "Join Group" and select the local group created by the designated user.
- Once the desired users have joined the local group, the group creator must then select "Start Communication."
- If there is software to update, all the user's software will be updated to match the most recent version of the group.
https://en-americas-support.nintend.../how-to-update-software-data-via-a-local-user
Note: you don't have to be updated for this to work, but I do believe you need to be at the same release number as the unhacked switch your using. I've used this method a number of times and it works great.
The other option would be to find "backed up" update and install, I think Tinfoil can be used for that. I haves used that method though so can't speak to it.