If a shiny works in my cafe, do they get the special outfits already obtained?

Question

So, in Pokémon cafe remix, Pelipper dropped me off a “stylish waiter” version of Sneasel. Which got me thinking, would a shiny wear other outfits already obtained?

I.E. If I obtained shiny Sneasel would he be able to wear that outfit? Or, would a shiny Eevee wear other Eevee outfits I already own? And if so, would a 5* chef outfit work for a shiny too??