This paper proposes a safe-passage cone-based guidance strategy developed in a relative velocity framework to enable a generic aerial robot execute a precision three-dimensional maneuver through a narrow orifice in a wall. The relative sizes of the robot and the orifice are such that the orifice is only slightly larger than the robot. The orifice is approximated as an elliptical shape, and analytical nonlinear guidance laws incorporating state-based switching are derived. It is demonstrated that the guidance laws developed can be used to maneuver the robot through both fixed and moving orifices as well as in scenarios when the orifice is closing with time.