Personally I wouldnt keep it secret, just invite both sets of parents.
I cancelled my big white wedding cause of being preggie and had a very small registry office wedding, my parents flew over and we just had them and my DH mum at the service, had lunch at home and my BIL came, went to a local restaurant in the eve where a friend and her family joined us, it was really nice.
We are still hoping to have a big church do/blessing next year.
hope you have a beautiful day whatever you decide.