No need. i believe you.
Strange the clearances are tighter, but oh well...
Well, I already did it so I might as well post a pic...
This was the tiniest size that I could find. Unfortunately the image doesn't do a good job of conveying how small the ball end is. It's really small. I actually had to try it with a couple of the same size because the little plastic ball kept breaking off when I tried to close the philips. Anyway, yeah. It won't close, sadly.