They'll cope. They were developped from woodland edge plants.
Just remember to plant the young currant plants deep
to encourage additional vertical shoots,
and,
really firm down the soil.
Otherwise you'll suffer from 'rootrock' and they seem never to establish/prosper.
Ask me how I know.
Small child in the garden so want to avoid toxic stuff, like the idea of currants though. How do they grow in shaded spots?