Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so.
goodness knows
- No one knows. (A variant of "God knows.")
Goodness knows how long it will take for my application to be processed.- It is true, certain, or definite that; it is obvious or clear that.
If you want to go aggressively secular, there is Fuck knows
fuck knows
(idiomatic, vulgar, followed by a wh-clause) I don't know; nobody knows; it is unclear. Fuck knows what we'll do now the car's broken down.
but while 'fuck knows' can substitute in many situations, the requirement for a subsequent wh-clause means it wouldn't work in your example construction.
