Single handle shower leaking from handle

[JustBad]

Have a one handle shower pouring water from handle, probably vintage 1964 or 1965. Tile enclosure, built up over what appears to be industrial-strength chicken wire covered in plaster. No way to turn water off, except at the main, so wondering what or even if there's a time-efficient way to replace the works that would cause the most minimal life interruptions. Initial thought would be to hire a professional to install shut-offs within the zinc piping then DIY from there, but interested in any suggestions I can get.

Thanks