If you find that the wire is too thick to grab the narrower stick, you could tie a prusik loop around the stake and hook into that.
The Prusik Loop is a climbing knot used to climb verticle ropes, but it will work on sticks like you have as long as the string or cord you use is thinner in diameter than the stick.
All you do is cut a short section of string or cord, tie the ends together, and then lay it flat against your stick. Then you wrap the loop around the stick and through the knot end a few times . Finally, you pull the loop itself to tighten the wrap down and now when you pull against the loop, either up or down, it tightens the wraps going around the rope or stick in your case, making for a pretty simply but effective sturdy connection point. When you release tension on the loop you'll be able to easily slide the whole thing up and down the stick making it completely adjustable.
So, how about that? Working a little bit of rope climbing into a grow thread and keeping it topical. Don't see that every day.