You will have to touch each computer, because the settings for the Toolbar buttons are saved within the local user's profile. However, you can copy the config file from your computer and simply place it on the user's computers to simplify things.
You can verify the location of your "Toolbars" config file within the registry. Navigate to the registry directory: HKEY_CURRENT_USER\Software\Laserfiche\Client8\Toolbars-Controls. Within that directory, there should be a REG_SZ key called 'Controls' with a value of the config file folder path. By default, it is in the following path:
There will be a file in there called "Toolbars"; you can copy that file from your computer and replace that file on the users' computers with your copy. That will switch their LF Client to showing the exact same toolbar buttons as your LF Client.
NOTE: If they had other buttons configured on their toolbar already that you didn't, then those buttons will go away! Again, it will make their toolbar buttons the exact same as yours.
Unfortunately, there is no centralized way to handle this, and there isn't a way to add just that one button to their Toolbar other than manually doing so within their client. It may be easier to draft up an instructions document for adding that button, then send it out to all of your LF users.