Can't connect all the dots but maybe I can shine a small amount of light. Here is a list of every player who wore #4 from their first year in Milwaukee in 1953 until they moved to Atlanta in 1966:

1953: Worn by Sid Gordon for 140 games

1954: Worn by Danny O'Connell for 146 games

1955: Worn by Danny O'Connell for some part of 124 games (he also wore #27 that season)

1956: Worn by Danny O'Connell for 139 games

1957: Worn by Danny O'Connell for 48 games and Red Schoendienst for 93 games

1958: Worn by Red Schoendienst for 106 games

1959: Worn by Red Schoendienst for 5 games

1960: Worn by Red Schoendienst for 68 games

1961: Not worn in a MLB game by any Braves Player

1962: Not worn in a MLB game by any Braves Player

1963: Not worn in a MLB game by any Braves Player

1964: Not worn in a MLB game by any Braves Player

1965: Not worn in a MLB game by any Braves Player

1966: Moved to Atlanta. No one wore it the first year either.

According the Baseball Almanac, the Boston Braves had an Indian head on their jerseys as of 1946 and didn't make any changes to their uniforms when they moved from Boston except changing the "B" to an "M" on their hats. The absence of the head according to this info may be a red flag.

Good luck in researching it. I would look a little closer for any remnants of stitching or glue residue. Hope I helped.