Missions to small bodies in the Solar System face a number of challenges as early as their inception begins, due to the lack of information that usually characterizes asteroids and comets that have never been the target of an in-situ mission or been observed from Earth in a favorable geometry. Robust mission design to these targets can only be achieved if uncertainties affecting the a-priori knowledge - or lack thereof - in the small body shapes and dynamical environments are correctly handled. Small body shape models, customarily represented as a collection of triangular facets or generalized through higher-order elements are a function of a mesh of control points effectively defining the shape. Describing this ensemble of control points as a multidimensional random variable, obeying a Gaussian distribution of known mean and covariance, enables performing linearized uncertainty quantification in the small body's inertia parameters and gravitational field, allowing valuable insight into the small body dynamical environment to be gained, at a lesser computational cost than a traditional Monte-Carlo sampling of the shape, to the benefit of mission designers and planetary scientists alike. Moving closer to the shape, the capability to autonomously survey a small body by means of Lidar observations given little to no a-priori information is demonstrated, in addition to the capacity to deliver a consistent shape estimate accounting for underlying errors in the reconstructed shape. This consistent pair of a shape estimate augmented with its uncertainty metric allows model-based navigation to take place in a robust manner, through the use of an Iterated Extended Kalman Filter taking in position and attitude measurements from a Consider Batch Filter augmenting the measurement covariance with a commensurate consider contribution coming from the shape uncertainty model. A sensitivity analysis covering a subset of the parameter space has validated the proposed framework's robustness, paving the way for autonomous mapping and navigation of small bodies in the presence of uncertainty.