Randomize a playlist

You can do that, if you build your playlist a little differently:
In the Web app, go to your tv show library and set it to ‘Episodes’ view mode.

Then activate the ‘Custom Filter’
then create a filter that includes all your cartoons
add a second filter criterium to include only unwatched episodes

Then click on the ‘Add to playlist’ icon and save this list under a new name.
You now have a ‘smart playlist’.

Now call up this playlist in your Plex client and let it play randomly.
The Playlist will automatically shrink as your episodes get played and their ‘watched’ status is set by Plex.

If you have seen all episodes, reset the ‘watched’ status of all the shows back to unwatched.
(This can be done for several whole shows in one sweep, so it is not that laborious.)