that picture does not have an integrated headset, and i don't believe that's what you are talking about. those races on the frame can be removed. your fork sounds like it's called a "1 inch threaded fork" the same fork used on bikes for deeeeeeeeeeeecades

if you can't accurately describe it because you don't know the terminology and you can't take pictures, it is going to be much more worth your time to take it to a local bike shop and ask them, instead of face the wrath of the SSFG forum.