Novel, optically responsive devices with a host of potential applications have been demonstrated by coupling carbon nanomaterials with photochromic molecules. For light-induced conductance switching in particular, we have recently shown that carbon nanotube-polymer nanocomposites containing azobenzene are very attractive and provide stable and non-degradable changes in conductivity over time at standard laboratory conditions. In these composites, the photoswitching mechanisms are based on light-induced changes in electronic properties and related to the Pool-Frenkel conduction mechanism. However, no link between conductivity switching and the molecular motion of azobenzene chromophores could be found due to application of high elastic modulus polymer matrices. Here we report on single wall carbon nanotube-polymer nanocomposites with a soft polycaprolactone polymer host. Such a system clearly shows the transfer of light-induced, nano-sized molecular motion to macroscopic thickness changes of the composite matrix. We demonstrate that these photomechanical effects can indeed overshadow the electronic effects in conductivity switching behavior and lead to a reversion of the conductivity switching direction near the percolation threshold.