Do I get to use non-bonus abilities from items I don't have equipped?
Page 6 of the Arkham Horror FAQ here says

Q: Do I have to be using the Bullwhip or Cross in combat to gain their special abilities?
A: No, in the case of these two cards, you do not have to use them in combat to make use of their secondary abilities.

This implies to me that any other such weapon that has a secondary ability (i.e. one that isn't +N to combat checks or something similar) can also be used similarly without being equipped.