 Born in Poznań Skowroński played for local side Warta Poznań advancing through the youth sides before leaving for Śmigły Wilno in 1938.In his second season with Śmigły the outbreak of World War II with the Invasion of Poland put Skowroński's career on hold until 1945.Śmigły Wilno was dissolved in 1939, with Vilnius () also becoming a Lithuanian city after the war ended.