Let’s put this assignement in a professional and legal environement.
There is two components regarding copyright in a recording.
One is the composition, the other is the sound recording itself.
We’re not using any sound from the original record so we will not need any mechanical license. In the other hand, we will need to pass throught APRA AMCOS.
There’s a bunch of licenses avaible depending on the use of the Sound A Like / Cover avaible online :
As we’re not planning to share this work publicly; none of the licenses can apply.
If ever we used it, we’ll need to go through APRA AMCOS to ensure the artists to get their share in the process.
References : APRA AMCOS / SASENC