Hi Lindsay: any of the UN agencies (UNDP or UNICEF are relevant in this instance) are global and secular, as is the Red Cross - they are deemed International Organisations. I'm not a fan of any of them (I worked in the aid world for a quite a while) - because the egos of their staff tends to get in the way of actually getting stuff done, plus they are very expensive (and lie about it). Oxfam is much better, as is CARE say. In the UK we have ActionAid, WaterAid and a plethora of others that are secular and impressive. Save the Children does some very good work too.
The good news is that some of the religious agencies are really very secular these days too. But it does change country to country so I tend to avoid them.