One source of mandrels for winding coils for chain making is.
Any industrial supply place (I am using MSC) selling drill rods in
1/16 increments and even finer. Cut them to convenient length and you
ready to go.
For more demanding tasks I use tail end of drill bits. I have a set
from 1mm to 10mm in 0.1mm increments. This gives me all the
flexibility that I need. Just wrap business end in leather before
using tail end as a mandrel.