I want to give a C++ programme to someone for testing but I don't want them to see the source just yet. My main issues are that I don't know what platform that person is using and I don't want to create a shared library unless I have no other option. Ideally, I would like to send headers and object files for the person to compile and link him/herself but as far as I know that would only work if the person has the same set up that I have.
I am currently using Windows but I'm comfortable working on any Unix-like system as well and I am not using an IDE, in case you need that information
Well, a Windows development environment allows you to bind some native always backward compatible winapi functions. The distribution of correctly setup binary .dll files, along with consistent headers, is enough.
For Linux distributions, the scenario is different, since you need to have a distributed package compiled from source (that's disclosed), or distributed binaries for every Linux distributions you actually want to support.
If you want to avoid source code disclosure, where it's needed to compile on specific target systems, use a licencing mechanism that's preventing to run it.