With a scripting language like AutoIT or AutoHotkey, it's possible to close the (invisible) window with the caption/title "HWiNFO64 v<version_and_build_number>", e.g. "HWiNFO64 v6.28-4200" for the current stable version. I just checked in WinSpy++ if I can find the window and close it and it works (although I tested with an older HWiNFO version).
Example for AutoIT:
$ver = "6.28-4200"
WinClose("HWiNFO64 v" & $ver)
Could be improved by getting the version number from the running EXE, but this was just a quick test and example.