While spindle-whorls are common archaeological finds, and while there are hundreds of dozens of spindles in all kinds of homes, working or not, the spindles themselves - that is, the sticks - are not something commonly seen for sale on markets. Medieval spindles are usually rather slender with a double-conical form. With as little as two or three millimetres diameter at the ends, and not much more than a centimetre at the thickest place, they are too slim to be turned on just any lathe - the thin stick starts to wobble, making an efficient production difficult or impossible. But spinning with a much thicker double-conical spindle stick, which would pose no problems when turning, will not work as well. Even more important, that stick won't fit the whorls so smoothly. And you want your spindle to fit your whorls, all of them, so you can just change. Hints on how to fix the spindlewhorls to the spindle and how to wind yarn on it can be found here.
These spindle sticks are modeled after a find from the Mühlberg-Ensemble in Kempten, Germany, where a lot of objects - including a number of spindle sticks - were found in blind floors of the building ensemble. This particular stick is c 20 cm long and has a maximum diameter of c 15 mm, so it is a little shorter and thicker than my long spindle sticks. It is available in birch or maple wood. It weighs about 7-9 g.
With the removable whorl, you can for example have three spindle sticks, spin with one until it's full, spin with the second until it's full, and then ply both singles together on the third stick before removing your plied yarn from that spindle, freeing all three again. That will work only if you can change your whorl from spindle stick to spindle stick - and preferably, if you have more than one whorl, this would work with any of your stash.
In contrast, most modern spindles are seen differently, with the whorl and the spindle stick firmly belonging together. Most spindle makers just have their own method that will cut out the need for double-conical spindle sticks - often they use a stick that is firmly fixed to the whorl and not conical in shape.
However, if you prefer to use and store your spindles the medieval way, here is a spindle stick with the required double-conical form. They are made from wood, using modern machinery, and sanded to smoothness but not treated in any other way. You can either leave them untreated and use them that way or finish them with your choice of oil or wax.