This is a minefield, isn't it? My DS1 doesn't have eczema any more now that his (food) allergies are under control, but he does react to various suncreams with hives, itching and subsequent nasty eczema. Nothing really dangerous - so far - but it's nasty and uncomfortable for him.
Suncream is so ridiculously expensive, and I can't afford to keep buying whole bottles of different brands just to try a little bit on his wrist. Mostly, I keep both my boys out of the sun between 11am and 3pm, so try to avoid the need for it (and luckily there is lots of shade in our Reception school play area) - but this isn't always possible.
Various friends have been helpful over the years, letting me put just a dab of their chidren's suncream on DS1's wrist to see what happens. Have never found one which works for long though. Today we tried a Boots own brand (horrible itching and a red rash) and an Avon 50 factor Sun+ (absolutely fine, have been given what's left in the bottle, and will be trying it again tomorrow 
)
I wish the ingredients on suncream and other toiletries were easier to understand. The manufacturers seem to delight in using long and complicated sciency-sounding names for quite ordinary ingredients (e.g. calling water "Aqua" and hiding all nut ingredients behind chemical words and other gobbledygook that no ordinary person understands).
From reading these boards over the years, different children react to different things, and there is no one safe recommendation that you can follow. So... good luck with this!!