I suspect a ladies golf swing would not have been then what it is today. The corset alone would somewhat restrict the followthrough of the swing. My guess (and this is just a guess) that it would have been more "lady-like" putting, but I could be totally wrong. 19th century women did all kinds of things in corsets and fully dressed like tennis, badminton and fencing, but I strongly suspect that it was not with the kind of athletic mobility that you would see from someone like Serena Williams.
It wasn't regarded as lady-like to run even as late as the 1920's. My grandmother told me once that she loved to run and would do it for the love of it and when people would stop her to ask why she was running (yes they really did!) she would tell them she was going to miss the street car! She was born in 1906. I'll see if I can find something more on this.