One can use the extension Toggle to create the keyboard shortcut for wrap tabs as follows.

1. Install the Toggle Extension.

2. Open the keybindings.json file:

3. Add the following in the keybindings.json file. It will create "Shift+Alt+W" keybinding to toggle the wrapping of tabs:

{
    "key": "shift+alt+w",
    "command": "toggle",
    "args": {
        "id": "wrapTabs",
        "value": [
            {
                "workbench.editor.wrapTabs": true
            },
            {
                "workbench.editor.wrapTabs": false
            }
        ]
    }
},