As an American I consistently say /ˈʃæmən/ and don't recall ever hearing anyone, American or otherwise, saying /ˈʃeɪmən/.
The latter might be a regional difference? I've lived in a half dozen or so different places and haven't come across it. Still, I haven't covered them all.
Per Peter Shor's comment /ˈʃeɪmən/ is the primary pronunciation in at least one dictionary of British English.
Note: Since I relied on personal experience as a native speaker for this answer I'll mention that my formative speaking years were spent in the Northeastern United States and that I have spent significant time living in the South Atlantic, Midwest, and Mountain regions of my country. I consume media mostly in American and British English.