There's no way around this.
Spoke too soon. I'll get back to you after further investigation.
There's another Wine bug where invoking a .lnk file with SEE_MASK_NO_CONSOLE will create a console. That doesn't happen on Windows. I'll send a patch for that.
If I fix that bug and use SEE_MASK_NO_CONSOLE when calling ShellExecuteEx from the tests, I still get some console windows. If I also hack ShellExecuteA to use SEE_MASK_NO_CONSOLE, I don't get any console windows, but my testing on Windows has shown that to be incorrect. So, there are a few things I can do to mitigate this, and I will send patches for them, but I can't prevent all consoles from being created.