"It's a big blow … but you've got to have confidence in the squad.
"Throughout the year we've been able to put in performances without Kane, so that won't be an excuse. He's a world-class player and quality leader, but our side's got to be good enough to cope."
Hesson said Central Districts' George Worker had been the first player considered as a replacement, but ruled himself out after standing on a ball during the Ford Trophy final at New Plymouth on the weekend.
Southee was considered the best option as stand-in skipper, despite Tom Latham leading the team during the Ireland-Bangladesh tri-series last May.
Southee and Williamson were involved in the Indian Premier League at the time.
"Tom's got plenty on his plate at the moment, [wicket]keeping and changing to batting in the middle order," Hesson said.
"Tim obviously did it [the captaincy] in the T20s earlier this summer, and did a good job."
Chapman's List A form had propelled him into the selection mix.
His Ford Trophy average of 80 was the highest for any player who batted more than three times. He had a strike rate of 103 from eight innings and was the only batsman to score two centuries during the tournament.
Chapman also helped guide Auckland to victory in the final against CD at Pukekura Park, scoring 47 from 36 balls and taking his best 50-over figures - three for 41 from eight overs of left-arm orthodox spin.