"p.o.v. a small group of British magicians who defined the wand (often conceived as a winged wand) as Air"
Yes, and more to that end, the wand is often equated with the wand of Hermes Trismegistus (also certainly Thoth):
"The ancient Egyptians knew HERMES as THOTH or TEHUTI, the divine personification of WISDOM. Portrayed as the ISBIS-HEADED scribe of the gods, he was the inventor of HIEROGLYPHICS and the patron of the SACRED SCIENCES of GEOMETRY, MATHEMATICS, ASTRONOMY, MEDICINE, MAGIC, and ALCHEMY. Thoth exists at every level of being. He serves the gods but he also preceded them. Indeed, he brought them into BEING, for he is the self-creating ARCH-MAGICIAN. He has but to NAME a thing and it SPRINGS into LIFE. He is the cosmic alchemist, the INNER and OUTER TEACHER, the BALANCING POINT between all POLARITIES"
-from Francis Melville, The Secrets of High Magic, Copywrite 2002, 2003. (and yes, he used that same scheme of irritating Capitalization and italics. Through the whole book.)
I should also note that, despite giving Kameas for Sol, Mercury, Venus and Luna, he omits Saturn Jupiter and Mars, saying
" You will notice that those (kameas) for Saturn, Jupiter and Mars are omitted. this is because the spirits associated with those spheres are extremely difficult to connect with for talismanic purposes Those of Mars are dangerous because they are difficult to control, and those of Jupiter and Saturn are too remote and abstract from a human point of view for any but the most experienced and skillful mages to be able to engage successfully. "
Despite that he has already given the Hexagrams and Correspondances for all seven Astrological Lords.