I would assume the lip-synching gives “chizuk” to others who are dancing and singing. People generally like to fit in with others. So I look at your lip synching more as a white lie (in order to do good for the sibor), which we know in some cases is fully permissible.
BTW, I think your question is not out of the realm of asking your LOR a shaila. Not that the CR isn’t full of people who play poskim on tv. 🙂