Unless Sharkey got very lucky with his rough-house tactics, Jackson would comfortably spear him into the canvas. Jackson possessed all the ring savvy of Corbett with none of the physical burdens - Jackson was made of stone and could dig. As game as Sharkey was, he would be in trouble here.
Sharkey would suffer the same fate as Frank Slavin "The Sydney Cornstalk". Only it might be quicker. Both Fitzsimmons and Ruhlin KO'd the sailor with a shot to the solar plexus, Jackson would do the same.
I think Sharkey was a bit tougher than Slavin was, and we know he could go at least 20+ rounds. In a finish fight, the outcome might hinge on Jackson putting Sharkey away before he gasses as he did at about round 23 vs Corbett. Though wild, Sharkey had a way of absolutely eating up quick boxing types like Joe Frazier did. While Sharkey was not as refined as Frazier, he was a two fisted brawler who sailed from pillar to post and gave his man no quarter. Sharkey got the better of Corbett, and ate up and spit out a tricky Kid McCoy. He got the better of a quick-footed Choyski too. This leads me to believe he could trouble Jackson, who really was not a strong clinch type of fighter or as fast and hard to catch as Corbett was. So who wins? Not sure. I might lean a tad to Sharkey on styles and stamina here. In 15 rounds or under I would pick Jackson via decision.