Not trying to be heartless here, just trying to point out that there are two sides to all stories, including tragic ones.
> You don't want to force them into signing anything,
Actually, you do. The more you give the employee a chance to mull over the whole thing, the more likely they are to lawyer up and hit you with a wrongful termination lawsuit. As the employer, I'd go one step further and if the CFO has allowed for a severance package of n dollars, I would initially offer them 90% of n if they sign right away and if they don't, give them the full n. Anything to get things settled right here, right now, in the room.
Most important is probably knowing the company and the individual you are dealing with. It's easy for people to misconstrue aggression as anger, which may or may not help your case.