I have added to the OP the steps for exporting and importing labels using Nunchuk Wallet. This software supports both the BIP-329 standard but also has a native export format.

* Nunchuk Wallet
Supports exporting labels: YES

Nunchuk supports exporting and importing labels in Nunchuk's export format or as JSON files according to the BIP-329 standard.

How to export labels with Nunchuk Wallet:

1. Open your wallet from the home screen.
2. Click on "View wallet config."
3. Click on the three dots in the upper right corner.
4. Click on "Export labels."
5. Select either the Nunchuk or BIP329 export format.
6. Enter the location where to save the .json file.

How to import labels with Nunchuk Wallet:

1. Open your wallet from the home screen.
2. Click on "View wallet config."
3. Click on the three dots in the upper right corner.
4. Click on "Import labels."
5. Select either the Nunchuk or BIP329 import format.
6. Find the location where you saved the .json file and import it.