Context is very important. I attended an LE training class when the "gunfight simulators" were first coming into use. They were testing a simulator called ROBBEC (I might not be remembering the name correctly) One of it's features was a sensor on the holster that told the system when you drew your weapon and that was compared with what the designer of the simulation thought was the first cue to draw. One scenario was you were arresting a cook at his place of employment on a warrant. The scenario started with you standing in the door of the kitchen and the cook was about 15 feet away on the other side of a large stainless steel prep table chopping vegetables with a chefs knife. The scenario played out with the cook running around the table and attacking the officer. He was shot every time and no officer was injured. However, every officer who ran that simulation was told they failed because they didn't draw as soon as they saw the cook chopping vegetables. In our after action review we explained that one could expect to find a cook with a knife in his hand at his place of employment and that the cook would have had to run around or jump across the prep table to get to the officer. We recommended that draw cue should be when the cook didn't put the knife down when commanded to by the officer standing in the door. I don't know if they ever changed it or even if that simulator ever made it into production.
In your example it shouldn't be considered a threat absent any other actions by the man carrying the axe.
I remember those days and the early judgment/decision-making, branching events. If the scenario was specifically that limited, meaning always requiring the officer(s) to approach the suspect in the commercial kitchen, it set up the officer(s) for failure, in a very real sense.
Taking into consideration tactical options potentially available in the real world, a properly designed branching scenario would've allowed the officer(s) to control how the suspect was confronted in the controlled environment of a commercial restaurant. In other words, not let the initial scenario influence an officer to do something that offered the opportunity to sidestep an avoidable officer safety risk. (Same reason bank robbery alarm calls were usually set up so responding officers (no sirens) arrived and called into the branch, directing an employee to come outside to discuss the alarm.
For example, knowing the suspect named in the BW/AW was present at the scenario 'kitchen', ask the employer (outside the kitchen area) to please call the kitchen employee out of the kitchen. The specifics of the 'where' would be driven by the layout and options within the premises. Stationing an officer (or officers) at whatever rear exit(s) might be connected to the kitchen, in case the suspect attempted to flee, could cover one eventuality. Then, the officer(s) making the arrest would be able to meet the suspect when he was called outside the kitchen by his employer. Sure, it's always possible the suspect might decide to carry a chef's knife to go meet his employer, but that's arguably a lesser likelihood than seeing officers enter and approach him in the kitchen.
I've had to go meet quite a number of suspects (BW's) and Restrained Persons (serving TRO's) at their places of employment, and when circumstances permitted, the first choice was always to have a supervisor (manager, owner, whatever) ask the employee to come meet him/her at an office or some other more isolated spot. It not only reduced the potential risks to other employees, should the employee being served/arrested become violent, but it reduced the potential for the employee to think bring tools/potential weapons, to meet a supervisor (manager, owner, etc), which weren't normally carried on their person during their work, away from their work station.
It worked out pretty handily over the years ... when the person being served/arrested
wasn't the manager or owner, of course.


It paid to know the employment capacity of the person we were looking for, though, as every now and again it might be the manager of owner. A little work and advance knowledge made it easier to set up the contact to
our best advantage. When the person was someone in supervision, management or ownership, we'd ask an employee to call them and ask them to meet a customer up front. Sure, we'd prefer to listen to the call conversation, to make sure a warning was included.

Never had a manager or owner come to meet a customer with a tool/weapon in their hands.
