Constantia would be a better fallback than Times New Roman for Garamond, and Corbel would arguably be a better fallback than Arial for Proxima Nova. They may also have Gill Sans installed with some software, plus Open Sans is not bad.
I'd put something like:
"Adobe Garamond Pro",Constantia,"Times New Roman",Times,serif
"Proxima Nova","Open Sans","Gill Sans MT","Gill Sans",Corbel,Arial,sans-serif
BUT you MUST remember to test your websites with each of these fallback fonts, because fonts often differ greatly in metrics.