"It was really nice to see that everybody was pulling in the same direction and was extremely supportive of it," said Vallverdu, who was signed up to coach women's world number three Karolina Pliskova this season.
"It's not normal in our sport to see everybody working together. So hopefully this would be a good platform so we can all in future have a little bit more connection when it comes down to the coaches at events or with the tour itself."
The second round of auction will also offer sessions with Wawrinka, Grigor Dimitrov and Feliciano Lopez as well as coaches like Carlos Moya and Toni Nadal, the uncle and former long-time coach of Rafa Nadal.
Fans can also bid for a frame featuring four signed rackets from Novak Djokovic, Roger Federer, Nadal and Murray with additional details available on ATP's website http://www.atptour.com.
"I am personally very happy to be involved," said former number one Murray. "So many areas of our sport have been affected throughout the Tour suspension, including coaches. It's important we help each other where we can."
Vallverdu sits on the ATP coaches committee, which will allocate the funds to the members who need it most. Some proceeds will also be donated to a global Covid-19 relief fund.
"This can be great platform to show that coaches can be a lot more involved on and off the court," said Vallverdu.
"The stronger message is that when we all work together, we can really achieve some big things for the sport."
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