would the shareholders be looking for the equitable remedy of specific performance in this case?
No. Specific performance is a remedy for breach of contract when the remedy is of a specific character and cannot be achieved by any other means or damages would not be a satisfactory remedy. It is for a failure to do something positive - usually the completion of a contract for a sale.
When you have a meeting, and the shareholders vote, does the company get a vote? No. How is the director appointed? By the vote.
When a contract is breached, what is the remedy? Damages.
How would a breach of contract - whether by the shareholders or by the company, invalidate the appointment?