Some people have placed their cones in a heavy coffee up. I agree with others who have an upper thread guide. There's no wobbling for me, when the thread is going up before it is being pulled back down. I have several thread holders and the ones with the heavy bases work the best. If the base is has no weight to it, then the thread doesn't pull straight and the cone stand can fall over. You could probably make your own if you are handy.
https://www.amazon.com/Embroidex-Adj...9863658&sr=8-5
This diy one looks pretty good.
https://www.bing.com/videos/search?q...tail&FORM=VIRE