Is there a way to simply open the game itself, instead of the Battle.net app on Windows 10, when you click on the desktop shortcut of HS?
Not really with Hearthstone, attempting to launch the executable manually will close the game software and start up the BattleNet App Launcher, because unlike the mobile version of the game, the App Launcher handles the game updates.
Other Blizzard games will prompt you to sign in at the start of the game. Furthermore, if the game software is not updated to the latest version it will not be able to operate. This is why it is always better to launch from the BattleNet app launcher.