Yes, before 1950 Lubavs mostly wore casquettes and other hats, but not shtreimlach.
The last rebbe wore a fedora because at the time it was modern, and he used to dress modern as part of his attempt to pass as a normal person. Once he became rebbe the chassidim tried to emulate him, so this ironically became frozen in time as the Lubav look.
For a comparison see the example of the Quakers, who in the early 18th century adopted a “plain” dress and manner of speech in order not to stand out, and then stuck with it as the fashions changed around them, so that 100 years later their “plain unobtrusive” dress and speech made them stick out like sore thumbs. Eventually they realized that they were achieving the exact opposite of their purpose, so they dropped it.
I’ve heard the story about the shtreimel, but don’t believe it. It’s perfectly true that his mother-in-law never approved of him, so the idea that she refused to give it to him is plausible, but I don’t believe he ever asked for it in the first place, because it’s inconsistent with the rest of the way he treated the nesi’us. He always acted and spoke as if he were not really the rebbe, so he would not have worn a shtreimel, which in Lubavitch was always reserved for the rebbe.