Well if you are going to speak to your cousin (who is marrying you), you had better speak to your parish priest, where you are living now (who will do your pre-nup) as even if your cousin says he doesn't mind not having one, the parish priest may still turn around and say you need it as he is doing the pre-nup enquiry.
We did the ACCORD one as well and the extent of the religious aspect was minimal, the priest came in for about an hour at the end and said a few words, mostly about the paperwork aspect, parts of the mass etc so there were no "lectures" if you like. Then we did a bit of ceremony to celebrate our engagement and the certs were handed out.
If your H2B is that worried and you do end up having to do one, put a post up here and see if anybody can recommend one with minimal religous content if possible (whilst still complying with your priest's wishes) as it probably does vary from place to place.
Another thing to mention is the pre-nup enquiry. This does ask some religious questions such as if you have children, will they be baptised in the RC faith etc. so to me, this is probably worse than the PM course (questions wise). I have a couple of friends who answered yes to this question and then went along and baptised their children in another faith but not every person might be okay with this "double standard" (sounds bad but you know what I mean