Staphylococcus aureus is an important opportunistic pathogen, responsible for a range of diseases that often prove challenging to treat due to resistance to methicillin, vancomycin, and other antimicrobials. Bacteriophages present a promising alternative to target such pathogens, particularly when conventional drugs are ineffective. The antimicrobial efficacy of phage therapeutics can be further improved through genetic engineering. Among S. aureus phages, members of the Twortvirinae subfamily, characterized by their strictly lytic nature and broad host range, are considered the most promising therapeutic candidates. However, their large genome sizes make them notoriously difficult to engineer. In this study, we utilized Twortvirus K as a model to develop an efficient phage engineering platform, leveraging homologous recombination and CRISPR-Cas9-assisted counterselection. As proof of principle, this platform was utilized to construct a nanoluciferase (nluc)-encoding reporter phage (K::nluc) and tested as a preliminary, bioluminescence-based approach for identifying viable Staphylococcus cells. Independent of their phage-resistance profile, 100% of tested clinical S. aureus isolates emitted bioluminescence upon K::nluc challenge. This diagnostic assay was further adapted to complex matrices such as human whole blood and bovine raw milk, simulating S. aureus detection scenarios in bacteremia and bovine mastitis. Beyond reporter phage-based diagnostics, our engineering technology opens avenues for the design and engineering of therapeutic Twortvirinae phages to combat drug-resistant S. aureus strains.