Is it permissible to cancel a vow to sponsor an orphan for the duration of a specific project, and pay an expiation instead, due to the need of a relative whose husband has passed away?

It is not permissible to revoke or retract a vow after it has been made. It must be fulfilled if the condition upon which it was contingent is met, as Allah Almighty says: "And let them fulfill their vows," and "They fulfill [their] vows and fear a Day whose evil will be widespread." Kinship ties can be maintained to the best of one's ability.