Can I do this is Inkscape? or would I be better off separating the layers using a photo editing software package (I don't have access to any paid ones).  

This is perfect for vector graphic and Inkscape, but needs some skills and a strategy to layout the hierarchy of layers.

Fantastic - do you know of a tutorial or something?

Not really; I´d search for Inkscape vector graphics for laser cutting for instance.

PS: and we have a special place inn this forum you might want to check out: https://inkscape.org/forums/cutplot/