I don't agree that the term 'with' is the critical element in this order. Each parent has responsibility for the child on day-to-day decisions when the child is in their care, which includes who the child is physically around during that time. It's immaterial that mum doesn't trust dad's friend, or dad doesn't trust mum's friend. If it's the child's time with dad, it's up to dad to determine what company the child keeps during that time, and mum is simply going to have to trust that dad isn't going to wilfully expose the child to a risk of harm.
I think you are risking a very expensive and very unnecessary contravention proceeding here. If it goes to Court, the judge is probably just going to clarify that order so you can't have creative licence with its interpretation, and make an order for costs against you, and who knows what that might include? If the father has already purchased the necessary provisions to accommodate the child's travel, you may end up having to reimburse the father for that, in addition to his legal bills.
I'd wager your best option here is to simply accept that, just like you, the father has a responsibility to keep his own child safe. Just because you don't know the person, doesn't mean they pose a risk of harm to your kid.