Declaring war is officially subject to congressional approval. what duty or role have presidents since abraham lincoln used in conjunction with the commander in chief clause to wage war without such approval?

The answer is duty to "take Care the Laws be faithfully executed" to wage war.

The president is "President of the Army and Navy of the US." While the Constitution particularly allows Congress the specialist to pronounce war, presidents since Abraham Lincoln have utilized the president condition in conjunction with the chief executive's duty to "take Care the Laws be faithfully executed" to wage war.  War Powers Act Passed by Congress in 1973; the president is constrained in the sending of troops abroad to a 60 day term in peace time (which can be reached out for an additional 30 days to allow withdrawal) unless Congress expressly gives its endorsement for a more extended period. Presidents have endeavored to demand that the Wars Power Act is an unlawful encroachment of their official power.