We employ polarization-resolved Raman spectroscopy to study the multiband stoichiometric Tc = 35 K superconductor CaKFe4As4. We do not detect Pomeranchuk-like electronic nematic fluctuations which were universally observed in the XY (B2g) symmetry Raman response for most families of the Fe-based superconductors. In the superconducting state we observe, consistent with a nodeless order parameter, a full spectral weight suppression at low energies and the emergence of a composite pair-breaking coherence feature at energies between 12 and 20 meV. We analyze the superconductivity-induced phonon self-energy effects and give an estimation for the electron-phonon coupling constant λΓ=0.0015 which is insufficient to provide attraction for high-Tc pairing.