What do you mean by cooling period: Is it Notice Period?
Is it not mandatory to sign any agreement any time during employment including notice period.
Employee can decline any clause or any agreement.
Non Compete clause/agreement may very well operate during period of employment.
Indian courts have consistently been denying enforcing Non Compete clause/agreement post termination of employment as it hits right to earn and source of livelihood and Indian Contract Act.
Before the employee signs any clause/agreement it shall be appropriate to show the copy to a labor consultant/service lawyer, law firm specializing in such matters and let the lawyer go thru the language and statements and opine thereafter...............
The clauses/agreements on Non Solicitation, Data Protection etc..........................may be valid post termination of employment.