Optical phonons in nanoparticles with randomness of interatomic bonds are considered both analytically and numerically. For weak dilute disorder, two qualitatively different regimes of separated and overlapped levels are observed, resembling the case of random atomic masses investigated previously. At stronger and/or more dense disorder, the particles become essentially inhomogeneous, thus constituting a minimal model to describe an amorphous phase, where the picture of vibrational modes becomes more subtle. We concentrate here on the experimentally relevant case of a strong disorder located near the particle surface and formulate the core-shell model aimed to describe the ubiquitous phenomenon of particle surface amorphization. We observe a peculiar effect of volume optical phonons "repelling"from the disordered shell. It results in the Raman spectrum appearing in the form of a combination of narrow well-resolved peaks stemming from the quantized modes of a pure particle core (red-shifted due to its effective smaller size) and a wide pedestal-like signal from the disordered shell, placed primarily to the right of the main Raman peak.