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tokens: in SNRs. We also investigated the opposite problem assuming that this canonical paradigm is valid and put constraints on the parameter space spanned by the ambient gas density around the shock and electron-to-proton energy fraction. Overall,the derived flux upper limits are not in contradiction with the canonical CR paradigm. Assuming this paradigm holds true, we can constrain typical ambient density values around shell-type SNRs to n ≤ 7 cm −3 and electron-to-proton energy fractions above 10 TeV to ε ep ≤ 5 × 10 −3 . Finally, we compared the presented flux upper limits to the flux measurements of the seven non-interacting shell-type SNRs detected both in the radio and VHE range. We found evidence of correlation between the ratio of VHE γ -ray luminosity to radio luminosity, ( L VHE ∕ L radio ), and source age. This correlation can be explained by invoking the theory of magnetic field amplification at SNR shocks, which accounts for the rapid decrease in radio luminosity by predicting a declining magnetic field strength as the shock slows down with increasing source age. Further development in the SNR population from the observational point of view should be achieved with the next generation instrument: the CTA observatory. In this work we have also estimated the performance of this future observatory to probe the ambient gas density and the SN blast energy parameter space. The results suggest that this instrument will be an important leap forward in the investigation of the Galactic SNRs and will likely be able to confirm or invalidate the CR paradigm. Appendix A Additional material Table A.1 Results overview. Notes. The SNR morphology type is indicated by S for shell-type and C for mixed morphology SNRs. The type of the latter is indicated as thermal (t), plerionic (p), or both (tp). If molecular cloud interaction is probable or certain (information taken from SNRcat), this is indicated by an asterisk. For sources with an observational live time ≲1 h, instrumental effects can impact the result and should be used with care. R ON are the radii of the circular analysis regions. Distance assumptions correspond to the arithmetic mean of the density range limits reported in SNRcat. Table A.2. Literature estimates on source ages, distances, and ambient densities. Notes. Some of the ambient density values are not direct measurements but are derived from fits to the X-ray spectra. In some cases correlations with high density gas clumps are observed or inferred. The corresponding densities inside the clumps are denoted by an asterisk. Table A.3. Spectral parameters of the shell-type SNRs detected in both the radio and VHE bands. Notes. Except for the value for RX J1713-3946, all radio flux density values are taken from Green’s catalogue Green (2014) . Also given are the references to the models applied in Sect. 5 . ( a ) Assuming a systematic flux error of 20%. ( b ) Sum of north-east and south-west regions. ( c ) Value from ( Acero et al. 2009 )