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Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so.

goodness knows
 

1. No one knows. (A variant of "God knows.")
   Goodness knows how long it will take for my application to be processed.

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.

Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so.

goodness knows

1. No one knows. (A variant of "God knows.")
   Goodness knows how long it will take for my application to be processed.
2. 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.

Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so. 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.

Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so.

goodness knows

1. No one knows. (A variant of "God knows.")
   Goodness knows how long it will take for my application to be processed.

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.

Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so. 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 eh-clause means it wouldn't work in your example construction.

Goodness knows is a derivation of God knows, so it is still 'religious' but not overtly so. 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.