This secular condolence letter is a great way to offer nonreligious sympathies.
I am so sorry about {Name}'s passing. I know there is no way to know what happens to us after this life, but I hope that it is a comfort to remember that {Name} made the absolute most of {his/her} time here on earth.
I want to offer my help in any way possible. I'd like to call on you next week if you're up to having visitors. My condolences for this terrible loss.