Shortcuts created in System Preferences will only work globally with applications that have matching Strikethrough options in their menu. This is not a feature that all rich text editors provide, thus the inconsistencies you experienced.
Nevertheless, TextExpander does support rich text formatting. When creating a new snippet click the "Content" header above the snippet and select "Formatted Text, Pictures." You could use this to store a small sample of strikethrough text to use the formatting of. This is sort of a painful workaround, but it should suffice in the majority of applications. You will probably encounter a few exceptions where this will not work.
The simplest solution is built into Mountain Lion. Select any text in a rich text editor and
CTRL+Click (right-click) on it. Select the Font>Styles
A new menu pops up. Select "Favorite Styles" and then select "Struck through" from the drop down menu. Now click Apply.
Your text will now be struck through. Keep in mind this Font menu may not appear in all rich text editors and others may not display struck through text at all.