Air taxi pilot reported a ground collision with an object during taxi. The object was hit by the propeller and the pilot shut down the engine.

Narrative

A Company Aircraft Y had landed before me and off-loaded bypass on the ramp. I taxied into the ramp as Aircraft Y was taxiing out; I saw the bypass and purposely park into the wind by the hanger to give myself plenty of space to taxi out and avoid the bypass. I had planned to turn right and taxi to the west side of the ramp after start up. After off-loading my bypass; putting up seats; and loading my passenger; I did a full walk around. Starting inside the back of the airplane; making sure my passenger knew how to use the seat belt; locking the cargo door; and securing the net; then closed the passenger door; removed the tail stand; locked and checked all the pods; cleared my off-loaded bypass away from the tire; checked the prop for nicks and clearance; walked to the far right side of the airplane to verify no tall stand; turned to look towards the runway entry to make sure it was clear; took two steps backwards and made sure there was nothing else in the way of the front of the airplane or wings (such as people or dogs). I'm pretty sure I even saw the Company bypass but it didn't completely register because my mind was on other things. I got in; gave my passenger brief; did paperwork; started up and waited for my avionics to load before I even released my parking brake. By the time I started taxing I had completely forgotten about the Company bypass and my taxi plan; I subconsciously reverted back to taxiing the route that I usually go to reduce prop blasting the agents. I was looking out the window while taxing; I was looking at the wind sock thinking about which direction to take off when I heard the prop hit the box and saw toilet paper flying. I immediately shut down. Cause: FatigueSuggestion: I wrote myself notes yesterday during the last flight to help myself remember import information when I was tired. I should have written myself a note about the Company bypass and not relied on my memory during the end of shift.