Found a trick/hack!
<#@ output extension="https://stackoverflow.com/" #>
or
<#@ output extension="\\" #>
Visual Studio neither outputs the default file nor complains about its inability too much.
If you want to avoid warnings, you can also modify output path through the extension:
<#@ output extension="xml/../_" #>
The file will still be created and attached to the T4 file within the project hierarchy in Visual Studio, but you can put it into any directory.
P.S. I’ve tried it with T4MultiFile NuGet package, but it should work with T4Toolbox too, I think.