I used caster sugar, known as Baker's sugar in the US.
As this recipe makes several servings, the amount of sugar baby would actually be having per serving is small. However, I do understand your concerns. I'm an "everything in moderation" philsopher and feel that it is potentially damaging to get too hung-up about not giving him this or that. Having said that, I'm lucky that, so far, my lo has not had any bad reactions to foods that I've given him and I realise that some babies can't have certain foods.
It probably would be ok to omit the sugar, but I'd choose a sweeter variety of juice (eg apple rather than cranberry). Let me know if you try it without sugar and how successful it was.