If the ID of a non-integrated HS head tube is slightly over 1-1/4" (34mm) then it takes a 1-1/8 headset. Here's a link to headset dimensions for your reference.

The decision threaded or threadless is independent of the frame, and depends on the fork and type of stem used, though availability of threaded 1-1/8 forks and parts for them is extremely limited these days.

BTW- you don't need precision measuring tools, because there's only one size in this range to worry about.