Your GM was applying a houserule. There is nothing in the ability that limits you to only arcane items. It doesn’t even limit you to items carrying spells you know, or are on your list. Such a limitation isn’t from the rules, it’s from your GM. You will have to ask him about ways to get around it.
Ultimately, I think it’s a bad idea. Spells and items aren’t inherently arcane or divine, except for scrolls. Wands don’t usually care about that; they only care if the spell is on your spell list. And since cure moderate wounds is on a number of arcane spell lists (e.g. bard or witch), a wand of cure moderate wounds could easily be made by an arcane spellcaster rather than a divine one. The adventure path, however, will never specify this, because the rules don’t usually have it matter. That means that the GM has to make a judgment call on every wand or staff in the adventure path, and that’s tedious and prone to inconsistency.
As a player, I would also object because it removes some of my agency; I can no longer predict how my trait here is going to work. I am left to the whims of the GM on any particular item. In this case, I would feel like this wand was deemed divine on the spot to deny me the ability to use my trait, and that would not sit well with me. Then again, this comes down a lot to player-GM trust, which you should have anyway; I wouldn’t play with a GM I didn’t trust. If I trusted the GM, this would be fine. If I didn’t, or had my doubts, then this would be a red flag.