Thanks!
I wasnt sure if mage wands behave the same way as wizard towers since they specify that you prepare the spell.
Ive had a couple of situations where I have an action (and some mana to spare) for this effect.
All spells are prepared face down in the planning phase.
Note that the Mage Wand (and others) bind a spell that is not replaced during the planning phase. To change a spell bound to a Mage Wand, you must use a quick spell and spend three mana, as noted on the spell card.
You alternately may cast a new Mage Wand at which point the first one and the spell bound to it returns to your spell book. (This would require more mana, but could be done during deployment from a Battle Forge, for example, saving you the action and perhaps allowing you to use a different spell from your wand during the first quickcast phase.)
To answer your question, yes, changing the spell on a Mage Wand results in a hidden bound spell. However, you may not first remove the spell being changed out. You must first attach a new spell, and then the original spell goes back into your book. You may, of course, bring out the same type of spell to bind to the wand should you choose to do so, provided you have another in your book.
This is different from the way the Wizard's Tower works due to the text on those specific cards.