Anderson toiled with the bat to top score with 67 in New Zealand's second innings but could only deliver eight overs with the ball. He was eventually replaced in the field.
Bracewell has 55 wickets at an average of 35.10 in 19 tests and Wagner has 58 wickets at 34.48 in 16. Both delivered strong spells against Somerset and Worcestershire (Bracewell eight wickets at 27.75, Wagner six wickets at 28.16).
In the test batting stakes Bracewell averages 11.03 from 34 innings and Wagner 11.76 from 23. Bracewell dominates the first-class statistics (24.73 v 16.75) but Wagner is renowned for his adhesive qualities.
In essence they could opt for Wagner to offer more zeal as a left-arm like-for-like swap with Anderson, or Bracewell could be chosen on the basis of being a stronger all-rounder.
"Corey found bowling and fielding painful," Hesson said. "There will be a lot of rest and recovery between now and Friday. We won't be training much because we were effectively a bowler light in the test with Corey's injury."
Hesson indicated Matt Henry would earn a second test cap after completing match figures of six for 199 from 53.5 overs.
"He hasn't done anything to suggest otherwise. Matt performed extremely well. He ran in hard and created opportunities. He was a good foil for Trent [Boult] and Tim [Southee]."
Hesson lamented the loss but defended his players' performance, particularly during the second innings collapse.
"We expect a certain standard of performance and we're close to that but we're disappointed with the outcome, having been in the test until the end of the fifth day.
"I wouldn't say it slipped away. Day one we were behind, day two we were ahead, day three we had parity but day four was the turning point. We fought back on the fifth morning after being in trouble at 12-3 but we regrouped well then had a couple of chances to push on before losing Corey at a crucial time in the last session.
"It was a game of punch and counterpunch. It was a tough wicket to start on, especially when it swung. We took 20 wickets and scored 743 runs but the fourth day made the difference through Alastair Cook, Ben Stokes and Joe Root."
Hesson commended the efforts of Martin Guptill and Tom Latham for their 148-run first innings opening partnership, despite both falling for ducks within seven balls before New Zealand had scored in the second innings. He also supported spinner Mark Craig who took two wickets but conceded 173 runs in 46 overs.
"Mark didn't have his best test but he's an important member of our squad. He's played nine tests and won three of them for us. I'm sure he'll be disappointed with the way he bowled, but he got better as the test went on."