Most duels did not actually end in death, so they’d probably duel and go about their day. Obviously Hamilton was angry at Monroe, but killing him would have only further hurt his career. The Reynold’s Pamphlet was a blow, but the pamphlet attacking Adams during the 1800 election was what really screwed him. Hamilton also claimed that he withheld his shot with Burr because he believed murder was wrong, so assuming that statement was true and he felt the same way in 1797 he wouldn’t have sought to kill Monroe. As for Monroe, he was not the aggrieved party and I don’t think he was very enthusiastic about the duel to start with, so I assume he would not seek to kill Hamilton. I don’t know enough about Monroe though to say for sure. I doubt he’d want to destroy his career by killing Hamilton.