The wealth of recent data from imaging air Cherenkov telescopes (IACTs), ultra-high energy cosmic-ray experiments and neutrino telescopes have fuelled a renewed interest in hadronic emission models for gamma-loud blazars. We explore physically plausible solutions for a lepto-hadronic interpretation of the stationary emission from high-frequency peaked BL Lac objects (HBLs). The modelled spectral energy distributions are then searched for specific signatures at very high energies that could help to distinguish the hadronic origin of the emission from a standard leptonic scenario. By introducing a few basic constraints on parameters of the model, such as assuming the co-acceleration of electrons and protons, we significantly reduced the number of free parameters. We then systematically explored the parameter space of the size of the emission region and its magnetic field for two bright gamma-loud HBLs, PKS 2155-304 and Mrk 421. For all solutions close to equipartition between the energy densities of protons and of the magnetic field, and with acceptable jet power and light-crossing timescales, we inspected the spectral hardening in the multi-TeV domain from proton-photon induced cascades and muon-synchrotron emission inside the source. Very-high-energy spectra simulated with the available instrument functions from the future Cherenkov Telescope Array (CTA) were evaluated for detectable features as a function of exposure time, source redshift, and flux level. Over a large range of model parameters, the spectral hardening due to internal synchrotron-pair cascades, the cascade bump, should be detectable for acceptable exposure times with the future CTA for a few nearby and bright HBLs.
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