Use of dethatcher

I’m starting to kind of rebuild my lawn.
First step was to reduce the excessive amount of moss (used sulphur of iron which worked well) now I’m not sure if I use the dethatcher or does that ruin the turf (still too much humidity in the soil)?

I just bought the starter pack. The plan is to use the granular fertiliser first, before applying the liquids – open to any suggestions – I’m totally new to NZLA products.