Yes! An axe like that could come in handy.

Pulling the axe from the shield takes much less **** than you thought it would, the blade slides out of the gash smoothly and the balanced feel of the haft fits comfortably into your hand. Your first bit of quality plunder and you haven't even left the walls. You slide the axe into the empty loops that had been holding your javelins and started looking for a way off the wall into the city.

To your right is the sound of fighting as other men from your division are attacking a tower. There would surely be a stairwell in the tower and probably more quality weapons like the axe too.

Where the wall curves to the left you see an area where there are large cracks running all the way down the wall. You are confident that you could climb down there, but are a little worried that you could be attacked as you climbed. Further to the left you see a blazing fire where the next tower used to stand, no hope of climbing down there.