: . . .I will try balsa I guess, and if that doesn't work then I'll look at
: small green limbs.

Look for a willow tree. Branches are very supple, but, the better choice would be to find some shoots coming from the base. The taper on the shoots is fairly slight, so once you get the bark off the diameter of the "dowel" should be pretty even along the length.

When willow shoot were used commercially for rungs on windsor chairs, people used to have circular scrapers which were used as sizing dies for willow branches. You probalby can't find any, though.

You might be able to make one by drilling a 1/8th inch hole in a piece of steel, then burnish the edge like you would do on a cabinet scraper. Probably you won't be able to work with just one. You may need to make a few, going up in increments of 1/64th. Pulling the willow shoot through the progressively smaller holes will shave off the slight excess wood, giving you round dowels which are as flexible as you would like.

I leave it to you to figure how to hold them in position until they dry

Hope this helps.

PGJ