To get accurate analysis of oil samples, the temperature the sample is taken at is important.
I may be out of line on NFPA70E as it is not applicable in the country I operate in, if so I apologize in advance.
My understanding is that where the work is done by qualified persons related to the task, exceptions can be made to the Energized Electrical Work Permit provided there are appropriate safe work practices (Article 130.1 (A)(3))pg 24 of 70E.
If I was doing the work, I would start with the Hazard / Risk Evaluation Procedure on pg 107.
Most industrial transformers have enclosed metal terminal boxes, in this case approach boundaries are not an issue as there are no exposed conductors.
Where LV terminals are exposed, they are usually taped up, thus reducing the risk. At 4.16kV the RAB would be 660.4mm.
If any of the terminals are exposed, the Approach Boundaries of Table 130.2(C) come into play.