Nanostructured soft matter systems represent effective and long-lasting solutions with respect to traditional and often obsolete methodologies for the conservation of works of art. In particular, complex fluids such as micelles and microemulsions are the most performing media for the removal of organic materials from porous supports, like wall paintings or stones. In this Article, we report on the characterization of two systems, EAPC and XYL, which have shown good to optimal performances in the removal of organic polymers from wall paintings. EAPC is a five-components fluid composed of water, sodium dodecylsulfate (SDS), 1-pentanol (PeOH), propylene carbonate (PC), and ethyl acetate (EA), while XYL is a "classical" o/w microemulsion, where p-xylene droplets are stabilized in water by SDS and PeOH. Small-angle neutron scattering (SANS) with contrast variation is used to infer a detailed picture of the structure of these complex fluids, with a particular focus on the partition of the components between the bulk phase and the nanocompartments. We found that, differently from XYL, the EAPC system is neither a microemulsion nor a simple micellar solution, with the cosolvents partitioned between the dispersing phase and the disperse droplets. These different structural features play a key role in defining the cleaning effectiveness and specifically the kinetics of interaction between the nanofluid and the polymeric coating to be removed, which is of paramount importance for the application in the field. Both of these nanofluids are effective in polymer removal, but EAPC is considerably more efficient and versatile. The composition and the structure at the nanoscale determine the capability of removing a broad range of different polymer coatings from porous materials. A representative case study is here described, addressing a particularly challenging conservative issue, which is the removal of a multilayered aged coating that was irreversibly damaging the pictorial layer of the Annunciation Basilica in Nazareth.