We studied the deformation properties of single Pickering-emulsion droplets using a combination of Scanning Force Microscopy (SFM) in force spectroscopy mode and Reflection Interference Contrast Microscopy (RICM). The droplets were made from an oil-in-water emulsion system which was stabilized by cowpea mosaic virus (CPMV) particles; the interfacial particle layers were either native or crosslinked after interfacial assembly. A general problem in the interpretation of deformation measurements of such complex microcapsules is the fact that both surface tension and mechanical membrane tensions may contribute to the force response of the droplet against deformation. While of different nature, the two contributions are difficult to separate and their relative importance in Pickering droplet deformation is unknown. In our approach, the droplet shape can be reconstructed during deformation using the RICM data. This enables calculation of stress-strain relationships of the droplet surface and a comparison with a continuum mechanical shell theory. In these relations interfacial tensions are evidenced as an offset of membrane tension at zero deformation, while mechanical membrane-tensions increase for further deformation as expected by membrane theory. We find that for this particular system, interfacial tensions dominate the response to deformation.