As I see it, the difference between “dans” and “sur” is that if a person must enter a dwelling or building to get to the property in question, the word “dans” allows that. However, if the word “sur” is used, then this does not automatically allow a person to pass through a building. I'm not sure if this relates in any way to the right to search a building. That may be an entirely different matter. It merely concerns the right to enter or pass through a building to reach the place where duties can be discharged.
Therefore, I would be concerned, if we opted to go with “sur”, that persons would have access only to the land, and not to buildings. Access is not restricted by the use of the expression “dans une propriété privée”.