I have the Boomerang, Bombs, Arrows (No bow), red candle and the Whistle. Pressing X repeatedly allows me to cycle through my entire inventory, Z however will only cycle between Boomerang and Bombs.
May be a bug in the quest as it uses a custom subscreen and changes what items you can use depending on the environment you're in. (Requiem of Hyrule)
Where in the quest did you encounter this? We need to know which subscreen was in use.
The Path area leading to Dungeon 4 is one example, another would be the Cave area leading to the dungeon that contains the White Sword.
Update: Head to the Caves in Requiem of Hyrule and then head inside the little hut, the name of the area should be Mercenary. In here the Z key doesn't function correctly.
Definitely a quest issue. The subscreen used in those areas has the select attributes set up incorrectly.