Using hybrid simulations, we investigate the onset of fast reconnection between two cylindrical magnetic shells initially close to each other. This initial state mimics the plasma structure in High Energy Density Plasmas induced by a laser-target interaction and the associated self-generated magnetic field. We clearly observe that the classical quadrupolar structure of the out-of-plane magnetic field appears prior to the reconnection onset. Furthermore, a parametric study reveals that, with a non-coplanar initial magnetic topology, the reconnection onset is delayed and possibly suppressed. The relation between the out-of-plane magnetic field and the out-of-plane electric field is discussed.