“If you’re happy and you know it,” should always be followed by “and you really want to show it,” NOT “then your face will surely show it.”

Because if your *face* will surely *show* your happiness, why even do the other activities? The “face will show it” lyrical option presents a smile or joyful expression as a natural consequence of happiness, eliminating the need clapping, stomping, and hooray. We could all just sit around smiling. But with lyric option 2, if you’re happy AND you *really* want to show it, then doing the other activities builds onto the happiness. The clapping, stomping, and hooraying flow naturally from the desire of wanting to *really* show off the happiness.