For similar challenges, my problem has always been that I'm not using dowels or perfectly straightened sticks. I like the imperfections. But when attempting to drill a hole that is parallel to the axis of the stick, first, what part of the (crooked) stick defines the axis for your purpose? Then, how do I best secure that portion of the stick, cut the end perfectly perpendicular to it's axis, and finally drill a hole of the desired diameter perfectly centered (even if the stick isn't round an approximate center can be defined) and drilled parallel to the defined axis?
With some improvisation it can be done, but it seems that different sticks require different solutions to the problem.
If I were a fan of dowels and lathes, my dilemma would be solved.