The individual cones look as if they are sewn together with oversewing/casting, I think that the 'inside' angles could be ladder stitch, for those I would suggest that you find a nice long needle - a darner perhaps, or maybe you might want to try a curved needle if you can find one.
I'm not so sure about keeping you quiet, but it will certainly keep you out of mischief
By the way, I've found japanese ring thimble making to keep me out of mischief - as if I needed anything else to do