Can you work on a captivate project which has been written on a hp laptop then finish it off on a mac? For example do final edits and animation? Or do you need to use a non apple laptop with captivate on installed?

You should be alright, as long as you match his version of Captivate, and install any updates for Cp from Adobe.

The .cptx files are binary compatible, they will work across platforms supported by Adobe for the published OS supported by the software.

On a personal note, I'd suggest you bid with an hourly rate, or ask for well written documentation on what is expected. A project the client tried to author themselves may mean they didn't have time to focus; but more likely means they don't have realistic expectations of what can be done, in a limited amount of time.