As I understand from various SOM threads and posts; carrying a wand is not important, it is an Air Element instrument so, a feather will do or, just your two fingers together which are your index and middle finger combined, together and, extended and with your other fingers, including your thumb, are to be folded. Just the index finger alone is the symbol for the Athame. Some use a sword or a Staff (a long wand). Most Witches prefer to use the Athame. The Athame is a Fire element. I don't know why. It just is. Some other SOM member can illucidate on this. I have seen an Athame made out of wood, out of stone or of course, metal. The Athame is not sharp, it is not to cut anything but the ethereal plane and to inscribe a pentagram in the air, a magic circle or, whatever a Witch comes up to do with it.
I personally use the Athame to inscribe pentagrams at every compass point of my magic circle and I use my Wand to propel my spells. I have an SOM thread out on just "How To Use Your Wand" if you are more interested in wand use.
Anyway, hope this helps. Blessed be.