Accepting severance pay?

  BLUF: my company is offering a significant severance pay (think 2x annual salary) for any employee who is willing to resign. What should I do?

Since 2009, I work at a very large multinational in Europe, currently managing a team of 20 people. I am in my early 40s, I like my job, my performance is good and I have a good network both in the company as well as external due to my involvement in industry bodies. Prior to this role, I have worked for other international blue chip companies in different industries. I think I can find a new job outside relatively easily, but with some risk in terms of location and salary. 

The organization needs to reduce head count. For a number of reasons, the company cannot / will not make people redundant. Instead, there will be voluntary program: employees at all levels will be paid 2 annual salaries, regardless of tenure, if they voluntarily leave the organization. There is one caveat: The manager can veto an application for the severance pay. The employee can of course still leave, but without the golden handshake. 

2 questions: 

1) what should I do as an employee? Apply for the package and accept the risk that my boss might veto it and that this might leave the relationship damaged from his perspective and mine? Stay put and do nothing?

2) what should I do as a manager? There is an expectation that  2-3 people in my team should leave. I assume that my top performers, who will more easily find a new job outside, are more likely to be interested. What should I do to fulfill my obligations towards my people and the company?