We investigate lateral p-n junctions, electrostatically defined in 14-nm-wide HgTe-based quantum wells (QWs) with inverted band structure. The p-n junction resistances are close to h/2e2, consistent with some previous experiments on 8-10nm QWs, and the current-voltage characteristics are highly linear, indicating the transport via ballistic helical edge states. Shot noise measurements are performed in order to further verify the underlying transport mechanism. We discuss the role of unknown inelastic relaxation rates in the leads and in the edge channels for the correct interpretation of the noise data. Although the interpretation in favor of the helical edge states seems more consistent, a definite conclusion cannot be drawn based on the present experiment. Our approach looks promising for the study of short quasiballistic edges in topological insulators in suitable geometry.