What studio was used for filming?

I'd like to find out what studio (sound stages and backlot,) Edward Small used in filming The Man in the Iron Mask.

IMDB only lists Los Angeles County Arboretum & Botanical Gardens as the filming location. That may have been where the wooded scenes were filmed. But I'm interested in the rest of the locations.
Edward Small Productions used United Artists as the distributor (though he later threatened to strike against them due to unhappiness with his deal). And UA used many studios for its releases based on who was producing them, including Eagle-Lion films, who Small worked for later.

He had worked for RKO earlier, and did a number of movies with Universal and Columbia after this movie. And the stars in this, Louis Hayward, Joan Bennett & Warren William, worked for a variety of studios. Warren William was mostly WB from what I can tell, and Louis Hayward seemed to work largely for Edward Small.

I've done some searching but haven't come up with anything specific, just a lot of cross-connections (most of them involving Selznick and Schenck).
Does anyone have any knowledge of this?