Tim Southee and Corey Anderson are expected to be rested from the opening game of the five-match series against England at Edgbaston.
Martin Guptill also missed training overnight with an upset stomach. If he is ruled out, Tom Latham will open in his place.
Drama unfolded as New Zealand arrived at practice.
The main grandstand at Warwickshire's home ground was in the process of evacuation.
An oven caught fire while someone allegedly deep-fried chilli peppers. A source, perhaps with a sense of humour, suggested they were "red hot". No one was hurt, although a staff member was sent home as a precaution after suffering minor smoke inhalation.
The content of the subsequent media conferences was more bell pepper than habanero on the Scoville scale.
Brendon McCullum and Eoin Morgan, the respective captains of New Zealand and England, enjoy each other's company. No animosity spiced up the series.
McCullum confirmed Southee and Anderson were unlikely starters.
"Tim's probably not right for this one due to a heavy workload in the two tests," McCullum said. "Corey's struggling a bit with his back but should be right soon. We've got some exciting youngsters who will get an opportunity at some stage.
"Depending on which three, or maybe four [pace bowlers we use], we'll work out who will take the new ball and who will be effective in the third seamer role."
In Southee's absence, McClenaghan's experience means he shapes for a return ahead of Wheeler. He last played during the World Cup against Bangladesh.
The 28-year-old was a standout performer in the Mumbai Indians' Indian Premier League win. McClenaghan claimed three wickets for 25, including 15 dot balls from four overs in the defeat of the Chennai Super Kings in the final.
He translated that form to the warm-up match against Leicestershire, taking four for 31 from 9.3 overs. Three of the wickets were top order batsmen, but New Zealand had the luxury of defending 373. However, 43 dot balls out of 57 indicates batsmen struggled to get him away.
Wheeler is the other alternative, but frontline opening bowler Trent Boult is expected to play, as is Matt Henry as the remaining right-arm pace option. Nathan McCullum is likely to offer his tidy brand of off spin and lower order batting from No.8.
"He's got the potential to be outstanding," Brendon McCullum said of Wheeler. "He's in the Trent Boult-mould, swings the ball at a decent pace, and has fitted into the team seamlessly. Hopefully he'll get a chance [during the series] to prove he belongs at this level."
In Anderson's absence, Santner is the bona fide contender to fill the void left by the retirement of Daniel Vettori.
"He's an elegant left-hander who bowls some handy left-arm spin. He should get a few opportunities throughout the series and hopefully can perform from the get-go," McCullum said.
Santner impressed with 94 as a makeshift No 3 in the first-class match against Somerset and his record suggests he's capable of scoring quickly. He took two for 34 from his 10 overs after making four batting at No.6 against Leicestershire. Santner trained in his eponymous No.74 shirt.
Like McCullum, Morgan would not be drawn on definitive team selections but the England side has been picked with a view to play more aggressive cricket after failing to progress beyond World Cup pool play. Only six of that squad were called up for this series, although seven of the eight newcomers have played for England in some form. Wicketkeeper-batsman Sam Billings is the exception.
Morgan said they want to emulate what New Zealand achieved to make the World Cup final.
"That sort of cricket has driven the one-day game forward.
"99 percent of it is having the players to set the standard of being aggressive. We struggled to do that throughout the World Cup simply because we didn't perform well enough. The guys we have brought in do something different, and we want that to continue. If they play as well as they have in county cricket it will be exciting."
"I like the look of their squad," McCullum said. "It's a little bit raw but there are talented players who are aggressive with bat and ball. Judging by comments coming out of their camp, they're looking to branch out."
