I don't think any further details are needed.
If you are the employer you can choose how to pay your employees. Just give the appropriate notification to the employees involved. Once they are 1099 independent contractors you need to treat them as such. There are rules involved in determining the status of a 1099 independent contractor. Follow the rules and you will be fine.
My comments are NOT LEGAL ADVICE. They are for informational purposes only. Actual legal advice can only be provided after you have signed an engagement letter. Answering this question does not create an attorney client relationship. Remember that without attorney client privilege you could possibly divulge information that can hurt your legal rights in the future. I am a tax attorney in Miami Florida. I can help you with your federal tax issues via a secure client portal if required.
If you are going to have the individual do the same work, switching the individual from employee to independent contractor is asking for trouble - please see the post at the link below.
The direct answer to your question is that you ask the individual to complete IRS Form W-9, by which you obtain the applicable SSN or EIN.
This information does not constitute legal advice and does not establish an attorney-client relationship.
There is no form to note that employee status has terminated and independent contractor status has begun. But as one of the other lawyers has advised you, you should be very clear that the person is no longer an employee. Please check the IRS rules about when someone is an employee.