In his 1886 etymological dictionary of Slavic languages, Franz von Miklosich (Franc Miklošič) derives šapka (czapka) from Medieval Latin cappa but also mentions “Turkish šabka.” Miklošič was one of Max Vasmer’s sources for the etymology of шапка.
Four decades later, Alexander Brückner claimed in his etymological dictionary of the Polish language that czapka/šapka was a native, proto-Slavic word, to be found in some shape in every Slavic language. I suspect this hypothesis is a minority view today.