Usually not an issue but this playlist has 62 videos.
As of the time of posting this answer, it's possible to add the entire contents of a playlist to the Watch Later playlist in the same way that you would any other playlist, although it's only possible on the desktop web interface, not mobile web or the standard YouTube app. I'm unsure if a YouTube Red subscription adds this functionality or not.
For mobile devices
Open YouTube in your device's browser.
From here, continue with the process outlined below for desktop devices.
For desktop devices
Navigate to the playlist's page.
Add all to...option in the dropdown menu, then select the Watch Later playlist in the second dropdown.
You've now moved the entire contents of your playlist to the
Watch Later playlist.
I'm not aware of a way of doing this via the youtube UI (website). However you might be able to use the Youtube API. Access to the watch later list was introduced only in v2 of the API, v3 should also work. Note that since it's a private playlist you can only access it via an authenticated request.
This is no longer an option to do the solution listed. You can save an entire playlist but unfortunately you have to add the individual videos that are on any playlist to your "Watch Later" playlist (or add them to your queue which, coincidentally does allow you to dump your entire queue to a playlist including your "Watch Later" playlist, but you cannot queue up an entire playlist so even going that route does not work... at least as of 4/1/2020)