Yes it is possible..
Check out the guide
http://forums.elderscrollsonline.com/discussion/63690/the-new-character-what-skill-to-take-guide
Basically put a skill from the other weapon in your 6 slots.
also, does it matter what level the quests are? because theres a whole region i skipped and they are like level 5-8 quests. what if i go back and do it with the staff...