I was just thinking this, actually. Really, a spear should be even easier than that. Any sharp object (knife, axe, etc) and a shaft of wood, like a broom stick, or some kindling, etc... to make a "Simple Spear."

Then you could add complexity with using rope and a knife to make a broadhead spear or something.

Maybe combine a shaft and axe and rope to make a pole-ax...etc.

Really though... anyone's first response waking up defenseless in "I will eat your face" swarming-infected hostile territory would be to immediately make a weapon of some sort... any sort... even, like, a sock full of rocks.