I bulk buy Water Wipes on Amazon which makes them a bit less pricey. I do find them worth it, but that's also because my daughter has very bad eczema and so her skin is really sensitive. We've used water + cotton wool at home and Water Wipes out and about since day one and still do now at 18 months! (Morrisons do the cheapest big cotton wool pads).
I think it's not a bad idea to keep with them for the bit of extra expense for the first few weeks when their skin is so new and sensitive. Then maybe think about switching up a bit later on (but perhaps stay with it a bit longer if eczema does run in your family). You could always intersperse with cotton wool and water for non-messy nappies to make them last longer.
The Johnsons extra sensitive wipes aren't the same as water wipes and we do find that they irritate her sensitive skin more:
Water wipes ingredients: Water (99.9%), Grapefruit seed extract (0.1% - contains 0.002% Benzalkonium Chloride)
The ingredients of Johnsons Extra Sensitive are: Aqua, Glycerin, Coco-Glucoside, Glyceryl Oleate, Hydrogenated Palm Glycerides Citrate, Glyceryl Polyacrylate, Carbomer, Lauryl Glucoside, Polyglyceryl-2 Dipolyhydroxystearate, Citric Acid, Sodium Hydroxide, p-Anisic Acid, Tocopherol, Phenoxyethanol, Sodium Benzoate.
I'm sure they're fine for the majority of babies, but at 6 days old I'd stick with as gentle an option as possible for now.