I am trying send a shortcut with Actions.sendKeys, but it isn't working.
(New Actions(driver)).SendKeys(Keys.ALT, Keys.SHIFT, "z");
You can check this question to refer about this - Pressing Ctrl+A in Selenium WebDriver
Check the answer which uses the chord method. In your case, you can do this -
String selectAll = Keys.chord(Keys.ALT, Keys.SHIFT,"z");
driver.findElement(By.tagName("html")).sendKeys(selectAll);