Doubt whether many think they will go to Hell if they tell a lie, but everyone, devout or not is, or should be, conscious of being jailed for perjury and of the consequences should a material lie be discovered, so making it a secular statement is perfectly adequate for all.
Apart from the affirmation allowed in court, there has been a solemn, non-religious, declaration used in many legal documents since 1835, with no 'religious' alternative. This statutory declaration has to be signed by the person making it and witnessed by a solicitor. Lying in that declaration that the statement above it is true is punishable as a form of perjury. This declaration is commonly found with conveyances; it may be required, for example, when someone certifies that there is not to their knowledge any claim of a right of way or private right over the land being sold .