Hedge Wizard's Gloves? They don't have the fire keyword, but I think it's reasonable that using Prestidigitation to create a puff of flame would count as an arcane fire effect.
Also, a possible spoiler about how your DM might be misreading things. Not sure if you want to look at it or get your DM to:
The activation conditions just say "or possess an item that creates [an arcane fire] effect". They don't say anything about being able to use that item. It's up for interpretation, but your wand could qualify even though no one can use it.