How to carry a knife around a kitchen safely?
One should try not to situate the cutting station away from the sink.  Most of the time you clean what you are going to cut and you have scraps to put down the garbage disposal.  If you need to clean the knife you also need to clean the cutting board. 

If I had to carry a lone knife around I would extend my arm down the knife next to my thigh blade pointing behind me. I used to work as a cook and that is how I carried my knife to my station.  Coming back I would typically have a number of dirty items so I would just place the knife in the bus tray.

Other way is wrist bent with dull side of the knife against your forearm.

Mistake I see is people want to start cooking before they prep.  You start producing dirty pans and use up the prep area and things just go to shit.  Here is what I recommend: 


Clean (and disinfect) the kitchen. Sink counter, pots, and dishes
Soak and clean vegetables and fruit
Cut / prep vegetables and fruit and put them aside
Quick clean
Cut / prep meats (if marinade then do that first)
Cook - clean as you go 
One full sanitize
Assemble / serve