The fasces is a bundle of sticks sometimes with an axe in the middle. I presume you carried the bundle around with both hands, so how would have time to unpack and use the sticks or the axe if an angry mob is attacking you? I hope you can help, AH. Wikipedia says nothing on this.
The fasces did not really function as weapons (the stone axe heads were even removed when within the ceremonial borders of Rome) but were rather symbols of power and authority, as u/XenophonTheAthenian has written about in this older thread (focused on lictors) and u/ShallThunderintheSky in this more recent answer (on the objects themselves). If a magistrate was attacked he would simply have to trust that all of his aids, clients, personal attendants, and possibly hired gladiators or armed slaves could overpower the mob