Cautionary warning, regardless of what they decide, if something doesn't pass the small parts test, and comes off and a kid chokes, you will be liable.
Go to the CPSC.gov site. On the left column you will find CPSIA That link takes you to the CPSIA section. Tons and tons of information to wade thru. You can do a search for small parts testing. There is a 2 page blurb with diagrams of what a small parts testing tube looks like. If it fits inside the tube it's too small. You can send the buttons off to a CPSIA certified lab for testing, don't know the cost. I think you can get the tubes to test yourself, I'm not sure anymore.
Now buttons by and large are not considered choking hazards because for children's clothing they need to be small to work and because they are generally so small, even if they swallowed one, it would pass right on thru. The size you are talking about is not small.
My concern with covered buttons is making sure the fabric covered top stays on and doesn't come off. I stopped using them years ago, because they always seemed to come apart after using them for awhile. Maybe they have improved