Question about elastic to use for attaching removable pompom

I am finally finishing up the hats I have been working on for grandkids and sister-in-law. Thanks to Chris I made a pompom worth attaching to one of the hats. I had already purchased the buttons to use to make the pompom removeable so the hat can be reversible. However, the elastic that I have on hand is too side to work well for that. It is 1/4 inch wide.

As I have begun looking online for skinner elastic, I am finding both flat and round elastic. Which works best for this purpose. I also found elastic thread, but it looks really flimsy and I don't know how durable it would be.

Advice? Thoughts? Recommendations? Links? All welcome and appreciated.

TIA

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