But balsa isn't available as a dowel; it only comes in square or rectangular cross-sections. However.
1/16" hardwood dowels are still available in some hardware stores, and if you can't find those, cutting a round toothpick carefully in half on one of the tapered ends would yield you a perfectly round "dot stamp" of whatever size you needed up to roughly 3/32". (Or, you could get the same effect by running a small dowel into a pencil sharpener and then trimming it off to the diameter you wanted...)
Okay, I'm officially out of ideas at this point.