300 gp, by comparison to least crystal of return
This is a very difficult question, because none of the guidelines apply. Disguise self has access to any and all forms with the same body plan and size—that’s a huge variety of potential individuals. This isn’t half or a quarter or whatever of disguise self’s usual potential, it’s a literally infinitesimal portion. And you can’t compare its effect on Disguise checks against other items that provide a bonus on Disguise checks, for the same reason—Disguise can be used to make any disguise, not just the one.
Alternate form is very similar, except that’s a transmutation, and often a fairly substantial one. And, of course, it’s not a standard magical effect that appears in the item-pricing guidelines. So that’s no help.
Ultimately, though, we are talking about a pretty low value effect. Hat of disguise is great at its price—though I disagree with your feeling it should cost substantially more—but because of its flexibility. You can also get similar abilities as part of an LA +0 race (changeling), or as a 1st-level alternate class feature (egoist psion), the latter of which replaces a bonus feat. With just one form, it hasn’t got that substantial value. It’s not a considerable capability added to a character; it’s much more about characterization than it is about balance. We’re talking about something that is worth much, much less than a fairly cheap item, or low-level special features.
Thus, I’m looking at some of the lowest-value magic items that exist. The cheapest core magic item that isn’t consumable is hand of the mage at 900 gp, but frankly at-will mage hand is likely better than at-will single-form disguise self. And other books offer cheaper magic items, like some of Magic Item Compendium’s augmentation crystals that are as cheap as 100 gp (light like a torch) or 200 gp (+1 on saves against energy drain, inflict wounds, and death effects).
But the one that catches my eye is the least crystal of return, at 300 gp—that allows you to draw the weapon it’s attached to as a free action. That is, it’s Quick Draw, but only for a single weapon. That... sounds like a pretty similar situation as we have. And we already established that at-will disguise self can be gotten as a feat-equivalent, since that’s exactly the option that an egoist psion gets.