Wonder Guard has been ineligible to be Skill Swapped for ages now, but Entrainment has always permitted the passing of Wonder Guard. It's a nifty trick, but most stronger teams will be able to dismantle the strategy before it's able to fire. Using Taunt to prevent the support moves from happening, or just outright murdering the support Pokemon (in this case, Audino), does the trick. Even if Wonder Guard does get passed (or if Sturdy gets passed to a Shedinja), there are multiple ways to bypass it - Kyurem-B's Teravolt and Necrozma's Photon Geyser will both help you get around these strategies in a dire situation.
In the future, use the Overview and Q&A thread for questions like these. If you need help with your team, join the Smogon Doubles room on Pokemon Showdown, or check out the DOU Team Bazaar for ideas and sample teams.
I'll be locking this thread. If you need any further help, send me a message!