If there is no airbrushing on your tail you can clean your tail using pure rubbing alcohol and water mixed 50/50 and put in a spray bottle and then let it dry in the shade hanging.
If there is airbrushing you will have to take the stuffing out of the tail and use a mildly warm water and wool wash liquid mix.
Diaper with tail hole creation method (needs to be personally refined to suit your tail/diaper/body)->
What items you will need-
Diaper (preferably plastic backed)
Clear tape roughly 2+ inches wide
Now to make a diaper with a tail hole-
Unfold the diaper and lay it out without fluffing it
Cut with sharp scissors 4-5 Inches down the back of the diaper (depending on tail size)
Use the tape to cover what you have cut vertically
Use the tape across the inside first and then outside at the top to seal it up leaving a tail hole
If your tail is a belt or pin attached tail and you intend to use the diaper you are wearing then I recommend you wear 2 diapers. A safety diaper without any tail holes cut and wear the tail hole diaper over the top. Clothing will hide the belt slightly and pin on tails won't be noticed.
The other option is a plug tail... I think they are disposable tails so you could abuse it and you could wash in the shower without caring about destruction?