The thing is that Parent 2 already uses both languages on a daily basis, for work and for life. So in a worst case scenario the two just get mixed for the kid.
I think it's enough to use one to address to the kid. If the other is present in the environment the kid will learn it to some extent. But I think there is value in simplifying the first steps with language. It's a hell of a struggle. And scary if it does not go well/quick.
Avoiding one or the other isn’t really doable.