I've traced a reasonably messy oil leak back to - guess where - one of the oil cooler pipe to engine joins. To inspect and possibly replace do I need to drain the oil? - ie. will it all start gushing out if I remove? (I'm new to all this!).

You will lose a little bit that is in the pipes / cooler but no need to drain sump. Common leak point, just replace as repair means going to a specialist hose manufacturer.