I think you should reframe the whole situation. When you do not have the budget, replacing key employees is not something wise to do; you'd better figure out why you ended up with inadequate budget and seek ways to have the budget and keep your keep employees, rather than kick key employees.
That is, the logic of your boss is flawed and as long as you are trying to act according to it, your actions would be wrong as well.
Therefore you have two options:
a) given that you have tried already to persuade your boss, to no avail, accept doing what he asked you to do, but with written stipulation you'd not be held responsible for consequences. "If that happens I will be accountable for failing to deliver the project." - you should take action that you do not be held accountable.
b) consider what'd be the worst consequences when that key employee is removed. Bankruptcy? Shrinking the size of the company? Remaining in a mediocre, yet stable state?
You should have a strategy for each of those.
If you expect the company to go bankrupt withing six months, then start looking for a new job ASAP. It's always easier to find a satisfactory new job when you are already employed, rather than when you are unemployed.
If the worst thing to happen is a long-term state of mediocrity, then you'd better not argue, follow orders, pretend to feel ashamed when the boss reprimands you for poor performance and make the best use of your time in the company.