Linda said (relative to making mandrels from wood dowels),
Drill a hole thru at one end to thread the waste end.<<
I don't know how you're turning the dowel to wind the coil, but
consider this approach.
Cut a slot about 1/8 to 1/4 in deep & 1/16 in (.060) wide across
the end of a new dowel (now its no longer a dowel, but a
mandrel). The size isn't critical; it just needs to be large
enough to accomodate the wire sizes you use.
Install the slotted mandrel (slotted end out) in the chuck of a
coil winder or a variable speed drill.
Place the end of the wire you wish to coil in the slot & begin
winding. Slide the wire between the thumb & forefinger to
maintain tension & guide the wire onto the mandrel. Quit wrapping
when you have enough turns or the coil reaches the chuck.
Cut the wire supply from the coil close to the chuck & slide the
coil off the mandrel.
By counting the turns for the 1st coil, you get a close
approximation of the number of links you'll get when winding more
coils of the same guage wire. Whole lot better than ending a few
links short or lots of links over (bg).
I use metric sized mandrels.
It works for me.