How to apply written defaults to a Magic Mouse (com.apple.driver.AppleBluetoothMultitouch.mouse)?
I couldn't find any way to apply the changes, but you could also use UI scripting to change the setting.

tell application "System Events" to tell process "System Preferences"
    try
        set visible to false
    end try
    tell application "System Preferences" to reveal pane id "com.apple.preference.mouse"
    tell radio group 1 of window 1
        if value of radio button 1 is 1 then
            click radio button 2
        else
            click radio button 1
        end if
    end tell
end tell
quit application "System Preferences"