It appears the Apeda shots were taken at the New York City apartment of Chaplin's attorney, Nathan Burkan, during the early part of 1927. Notice the similarities between the following two photos. The one on the left was taken at Burkan's apartment during a press conference in January 1927 (following Charlie's nervous breakdown). The photo on the right is from the Apeda sitting. The statue in the background is the same in both.
But the clue that sealed the deal was the date on the Spanish film magazine Charlie is holding in this Apeda shot:
In this close-up (thanks, D.), you can see the date of Mayo (May) 1927 (click to enlarge).
I believe that's actress Billie Dove on the cover.