I'm still learning how to use tarot cards. I have a sort of "beginner-friendly" Rider Waite deck that comes with a guidebook. Anyway, it categorizes the Suit of Swords as corresponding with the element of Air and the Suit of Wands as corresponding with the element of Fire (although my deck uses the word Rods instead of Wands) and the art on the cards strongly reflects this. I think that this is the conventional way they're categorized, and I've read that the two tools and elements are different depending on your tradition, but I feel more comfortable connecting Wands with Air and Swords with Fire in my personal path. I plan on getting another deck in the future when I'm more comfortable with the cards' meanings. Do the meanings of the Suit of Swords and the Suit of Wands become different if you switch their corresponding elements?
First, to answer your question, yes they do become different if you switch the correspondences that you use. You would be essentially switching all the Fire cards to Air, and the Air cards to Fire.
Second, you are correct that there is a difference in traditions. Some use wands as fire, others as air. The discrepancy in Tarot lies with two issues: equating the sword and the dagger, and assuming that all wands mean the same thing.
In Tarot, the item associated with the element of Air is the sword. Traditionally, there were four specific "elemental weapons" for working with the elements: the pentacle for Earth, the cup for Water, the dagger for Air and the wand for Fire. Over time, the distinction between the sword and the dagger has become blurred. In Europe, where the Tarot developed, swords and daggers generally had the same shape: double edged, long and pointy. The difference lies in their use. Now, from a magical standpoint I agree that the sword is a tool of Fire. Actually, it is Mars. It's use, just like in mundane life, is to separate one thing from another, typically the head and body of your enemy. In magic it is much the same. You use it to separate the space that you are in, to separate you from forces that would cause you harm or trouble, to banish, etc. But a dagger, being smaller and more easily controlled, has more uses. It can also create. It can carve, help prepare your dinner, help provide shelter, etc. It is much more of a tool than just a killing tool and, therefore, falls under the influence of Air (Mind) rather than Fire (Inspiration). However, their similar shape, and the fact that the sword is more dramatic than a dagger, has caused it to become the main symbol of Air in the Tarot. I tend to remember that it is actually daggers rather than swords when I am using it.
As far as the wand goes, it is absolutely a symbol of directing will. We use it to direct energy in specific directions. This direction of will is a function of Fire. Now, that is not to say that every wand is a symbol of Fire. The caduceus wand, commonly seen in the medical profession, is absolutely a symbol of Air. There are others as well. However, in the instance of the Tarot, it is associated with Fire.
There are some other considerations to think of as well. Wood burns. Metal (typically) does not. Also, if you look at it from an alchemical perspective, Fire and Water are the two opposite, original forces and it is through the union of these forces that Air, and later Earth, are produced. In a similar way, to create the dagger (or sword) the metal must be heated with Fire and tempered with Water to make it useable by the mind, so that it becomes not just will but a focused will capable of doing work and creating effects.
Of course all of this is just to help you make the connection with the symbolism of the Tarot, not to change your view. Tarot is, at its essence, a divination tool. It is a common language that is used between the subconscious, which receives knowledge and information from the Divine, and the conscious. For it to be effective both the conscious and subconscious must be speaking the same language. That means, the meaning and interpretation of the symbols of the Tarot must be the same in both parts of the mind. Usually this is done through a combination of initiatory ritual and study with great effect. It can be done with just study given enough time and effort are applied. If you want to use symbolism that differs from the tradition you are in, or what is commonly accepted, that is fine. Just make sure that you spend plenty of time solidifying that symbolism in your mind so that it is effective in your interpretation.
Thank you! That's very insightful. But... no matter how much I learn about it, everything about a wand makes me think of Air and I can't let go of it for some reason. I keep associating a wand with thoughts and imagination rather than will and intent. Maybe it's because I use my own wand to practice creative visualization a lot? It makes a "woosh" sound when I swing it downward and when I lift it I keep unconsciously imagining the wind rising around me. I should probably think of the tarot cards as Rods instead of Wands. Rod sounds more firelike to me.