Taper the end. I use floral wire (for 7/64) folded over. I insert it into the center and out where I want. Slide the tapered end into the fold and hold in place until it starts getting pulled in. Then milk the body over the taper until it comes out the other end (where you put the wire through). Then milk it back down until the taper is back inside the core.
I think that makes sense.