Microsoft is quite finicky about which part of Visual Studio is allowed to be distributed independently cf. the Microsoft documentation for some aspects. Else, it might be possible to work without a Visual Studio installation on Windows, which would also be quite nice, but see some recent discussion in another forums topic.
If nobody else knows better, I would not count on cross compiling for Windows, also because there are other more important issues concerning Swift on Windows (regex literals, macros).
To my knowledge you can do CI pipelines for Windows on GitHub (it might a good idea to configure it to use cmd instead of power shell), or see what is possible with a (cost-free?) Azure account.
I do not think that wine would be good enough.