Not sure what model nikon you have.
Mine will export onboard stored data in xyz format (easting, northing,elevation, code (description).
If you are working in a projected coordinate system then you could import that straight into GIS system and work with that.
Its a long time since I used Esri so thats out of my area, but i do remember bring these files in.
If you are in ground coordinates then you could add a scale factor within the Nikon software and reprocess the raw data to give true grid coordinates.
Something to bear in mind obviously is any bearing datum must also be taken into account.
Are you working in the same bearing datum as the projection you are working in?
If not then that too could be corrected inside the Nikon befor exporting.
You need to be fully aware of what you are doing and I'd suggest an export of the raw coordinates before you start 'messing' with it.
Nikon doesn't change the raw data only the stored coordinates so that is secure.
Maybe a bit more explanation of what you are doing - grid/ ground distances, true bearings (azimuths - different countries mix these meanings), projected coordinate system etc.