In general, slotless items cost more because they eliminate the opportunity costs that item slots usually represent: since you can only use one item per slot, and combining separate effects into one item both costs 50% more and also involves “putting more eggs in one basket,” it makes sense that a slotless item would cost more still, 100% more in this case.1
As the magic item guidelines are just that, guidelines, this will not always be true of every item that does not happen to fall into one of the traditional item slots. For example, something you need to hold in your hand in order to get the bonus cannot truly be called slotless, because it interferes with weapons and shields and all manner of other useful things characters do with their hands, and because it is conditional and may not happen to be where it needs to be when you need the bonus. If a weapon must be drawn to grant a Dexterity bonus, it won’t improve your initiative when you’re surprised—that is a big downside. Such an item should cost less, rather than more, than a traditional item in a traditional slot giving the same bonus.
But that does not describe your sword, since your sword grants its bonus even while sheathed. There is no hard limit on the number of sheathed weapons you can carry, and while the GM will presumably limit things if you really go overboard, having one extra sheathed weapon—this sword—while using whatever weapon you actually want to use (assuming it is not this sword) is presumably not going to run into that limit. As such, since you can get the bonus without it interfering in any other item you want to use, yes, this item is slotless, and the ×2 multiplier should apply.
as “an ancient artifact” that you “must attune” and “only one at a time” can be attuned by any given character, you are talking about an exceptional case for which there are really no guidelines and that cannot be handled so simply as assigning a gold-piece value to it. The game has a name for such items: artifacts. And the game does not provide pricing information for them (they are, literally, “priceless”).
The primary consideration for this sword, since you cannot use one of the other swords at the same time, is going to be what the other ones do, and which of them is best. Since they are based on the legacy weapons from Tome of Battle, I can tell you that Desert Wind is definitely not the best of the weapons in that book—but more importantly, none of the weapons in that book are worth using, because Weapons of Legacy was a very poorly-written book. Hopefully your GM is not following Tome of Battle too closely in their design, particularly the “personal costs.” But regardless of how the GM is handling it, the important question for this sword is going to be comparison to the others, not comparison to a pile of gold.
By the same token, concerns about wealth by level get a little blurry around artifacts. They are clearly inestimably valuable, but they necessarily are given out by the GM and unique. Opportunity cost is the name of the game. If the sword means you no longer have to buy a belt of incredible dexterity +2, then it’s worth at least 4,000 gp and the GM should think of it as such. If it allows you to buy a belt of mighty constitution +2 instead of a belt of physical might +2, then it’s saved you 6,000 gp, and should probably be considered worth at least that much. If you have to buy a belt of incredible dexterity +4 or +6 anyway, then this feature is worthless and should be evaluated as such by the GM. If you never would have bought a belt of incredible dexterity, but now benefit from this bonus, it should be worth somewhere in between 0 and 4,000 gp. Unfortunately, figuring out exactly how much is going to be very specific to your character and the system offers little and less assistance in judging it.
On the other hand, the other reason you might need to know the item’s value is if you wanted to sell it. If you actually wanted to sell a unique artifact—whether this sword or something else—the real world has thoughts on how to handle pricing unique artifacts: namely, auctions. If that was your goal, as GM I would lay out a kind of quest for you to set up the auction, ensure everyone with the means and interest was aware of it, see to security, so on and so forth. D&D or Pathfinder isn’t really a great system for such a thing, but as a side-quest we’d make something work. And you would get a price based on bidding, which would be based on how well you hyped up the auction and got people willing to go and spend money. The Appraise skill would get a work-out for once!
- Please note that in D&D 3.5e, Magic Item Compendium actually waived the price premium on combining basic effects—like enhancements to Dexterity—with other items. Without the 50% premium on that, the 100% premium on slotless items of the same effect is much too high. How high it should be depends on how serious a risk item theft or destruction is in your campaign, but 50% seems like a clear maximum, and in most campaigns it should be quite a bit lower. Pathfinder has not re-implemented that rule, and in fact has gone strongly the other way by forcing ability score enhancements to only appear on two slots (belts for physical scores, headbands for mental scores), forcing the combining of magic effects—and the premium—far more than 3.5e ever did. This decision is indefensible; Paizo is wrong and Wizards of the Coast was right. For the sake of a better game, I strongly advise using the Magic Item Compendium rule. For details on why the MIC rule is superior, you can see the explanation given in that book for it, or search on this site where the issue has been discussed at some length.