I do not think that it is possible make wallet in Linux, which works also in Windows. The only way, which you can use is to install virtual machine in your Linux, then install Windows, and in Windows install wallet. Virtual machine soft you can find through Google search.
It is possible, the concept is well known and understood and called cross-compile [1]. You cant expect a dev to have every system available, not even as VM. I doubt however that there is anything special with cross-compiling core.
[1]
https://en.wikipedia.org/wiki/Cross_compiler