The beads you are weaving with sound like they are so tiny that they
are in danger of melting.
Using soldering irons and lead solder is a no-no in jewelry. I don't
think anyone on this list will give you directions on how to do it.
To hold the design in place on the wire, could you use a crimp bead,
and then cover the crimp bead with a larger bead with a large hole?
Otherwise, perhaps you could use epoxy to hold the end beads in
Metalsmith, Certified PMC Instructor
Hard to Find Tools for Metal Clay