We investigate the influence of Co intercalation and altermagnetic order on the lattice dynamics of the layered compound Co_(1/4)NbSe₂. Polarization-resolved Raman spectroscopy, supported by density-functional theory, enables identification of six Raman-active phonons. Co intercalation drives a substantial reconstruction of the vibrational spectrum through zone folding of NbSe₂ phonons, producing hybridized modes with mixed zone-center and zone-boundary character. Despite this, Co atoms do not participate in any Raman-active modes by symmetry, which is in marked contrast to related 1/3 compounds where intercalant modes do contribute to the Raman spectrum. Temperature-dependent Raman measurements across the altermagnetic transition show no discontinuities, which is consistent with short-range spin correlations in the quasi-one-dimensional Co chains. However, we find evidence for spin-phonon coupling in A_1g symmetry modes owing to their out-of-plane Se displacements. Our work demonstrates the substantial impact of intercalation on the vibrational properties of transition metal dichalcogenides and the presence of spin-phonon interactions in a newly discovered altermagnetic material.