John Bunyan was writing in allegorical form, so there is no mention of God, even though he was a devout believer. The strict nature of the allegory slips once in the Pilgrim's Progress, when Christian does actually pray. But that is a momentary lapse, basically he sticks to the concept, so there is no God or Christian workship about. It is all symnolic.
So, it is very much not a secular hymn. It is a Christian symbolic hymn. Though you can take it whatever way you like if it suits you.