Jake, my condolences to you. I had a similar wish from my mother who was not Christian - but our local crem chapel just removed the crucifix and other religious emblems (they had a cupboard with the emblems of different faiths). It does need clarifying with the FD though, in advance.
I agree with naomi, jeza - it's worth going now to an FD just for an exploratory visit, to ask what's the simplest thing they are allowed to offer. You don't want to have to be doing it when you need it, far better to plan in advance.
Our solicitors hold details of our funeral requirements, and our final resting place, alongside our Wills.