The Boston Public Library's Leslie Jones Collection has this photo of Teddy Ballgame crossing the plate.
Their description says:
Date created: 1955 - 1957 (approximate)Sounds like a challenge to me.
Summary: Boston Red Sox Ted Williams (#9) crossing home plate as teammate Jackie Jensen (#4) prepares to bat in front of unknown Kansas City Athletics catcher (#22) as unknown umpire looks on at Fenway Park.
The catcher was either Billy Shantz (1955) or Tim Thompson (1956-1957). Both wore the number 22 for Kansas City and both threw right handed.
A bit of research on retrosheet.org shows that there were just three games when Williams hit a HR while either of the men were catching while visiting Fenway during those years.
In 1956 Tim Thompson was behind the plate in the 6th inning on July 17. This game can be ruled out because Mickey Vernon was batting behind Ted Williams.
In 1955 things were a bit different. In mid June Ted Williams had two games in which he hit a HR. Both of those games had Billy Shantz at the plate and Jackie Jensen following Ted in the lineup.
June 14, 1955
June 16, 1955
Based on that info I'd say that the catcher is Billy Shantz.
Depending which game it is the umpire was either Bill Summers (June 14) or Ed Runge (June 16).
Image courtesy of the Boston Public Library, Leslie Jones Collection.