You can customize the Hypershade so that the Script Editor appears as a tab in the Hypershade window. This tab is not retained in the Hypershade past the current instance of the Hypershade. While your Script Editor is in the Hypershade, it cannot be opened separately.

Open the Script Editor and the Hypershade. If your Hypershade is floating, run the following command to create a Script Editor tab in your Hypershade:

setParent hyperShadePanel1Window|TearOffPane|hyperShadePanel1|mainForm|mainPane|createBarWrapForm|createAndOrganizeForm|createAndOrganizeTabs;
$layOut1 = `paneLayout -configuration "single"  "scriptEditor"`; setParent $layOut1; control -e  -p $layOut1 scriptEditorPanel1Window;

If your Hypershade is in a pane, run the following command instead:

setParent MayaWindow|formLayout1|viewPanes|hyperShadePanel1|mainForm|mainPane|createBarWrapForm|createAndOrganizeForm|createAndOrganizeTabs;
$layOut1 = `paneLayout -configuration "single"  "scriptEditor"`; setParent $layOut1; control -e  -p $layOut1 scriptEditorPanel1Window;

To remove this tab, close or tear off the Hypershade. The Script Editor will be accessible from Windows > General Editors > Script Editor or from the Script Editor icon again.