Other arguments aside attached is a pdf of my ramblings (no pun intended) regarding Gallagher and what he may have known about walking shoes and how they might differ male against female.
This is a work in progress based on walking/walking shoes in the UK and DOES NOT look at what shoes AE may or may not have had on the final flight.
Chris, thank you. This is exactly the kind of genuine, thoughtful, primary source research this forum is intended to inspire. Understanding the cultural context in which Gallagher made reference to a "stoutish walking shoe or heavy sandal" is essential to any informed discussion of the object he was attempting to describe. It does appear that in the interwar years there was in Britain a surge in the popularity of recreational hiking or "tramping," as an outdoor sport. Footwear manufacturer's responded to the demand by offering "walking shoes" which, as your research shows, were not heavy hiking boots but ordinary shoes that were "stouter" than every-day styles.
The sport became popular enough that it's allure was celebrated in songs like The Uist Tramping Song.
Oh now gaily sings the lark and the sky is all awake
With the promise of the day as the road we gladly take
So it's heel and toe and forward bidding farewell to the town
And the welcome that awaits us ere the sun goes down
Come along, come along, let us foot it out together
Come along, come along, be it fair or stormy weather
With the hills o' home before us and the purple o' the heather
Let us sing a happy chorus, come along
It's the smell of sea and shore, it's the tang of bog and peat
It's the scent of brier and myrtle that puts magic in our feet
So it's home we go rejoicing over bracken over stile
And it's soon we will be footing out that last long mile