Full-back Gareth Thomas is set to train tomorrow in an attempt to prove his fitness after receiving positive news on his twisted knee.
But lock Robert Sidoli requires shoulder surgery and is not only out of contention for the All Blacks game but he could be sidelined for up to 10 weeks.
Sidoli now faces a race against time to be fit for the start of the RBS 6 Nations Championship, which starts against Ireland on February 4.
Wales team physio Mark Davies said: "Robert has had problems with his shoulder which we have been managing for a period of time but he has now aggravated it to the extent that surgical intervention is required.
"The injury is no longer responsive to conservative treatment and it is in the player's best interests to undergo surgery which should see him in recovery for eight to 10 weeks."
Thomas received encouraging news after undergoing a scan on the twisted knee he suffered in Friday's 61-26 win over Canada.
But the Toulouse full-back must come through tomorrow's session unscathed in order to prove he is fit for selection.
Wales name their team to face the All Blacks first thing on Wednesday morning and Davies explained: "Gareth knows he needs to team train tomorrow and we will further assess him after that."
Sonny Parker missed training with a groin problem and will be further assessed on Wednesday.
But there was great news for Jones, who returned to training after missing the last two games with knee ligament damage, suffered in the 29-29 draw with Australia.
And Henson was also back in action after being forced out of the Canada game with an infected toe.
Davies said: "Stephen has responded well to an extended period of rest and should be able to take a full part in preparations ahead of the New Zealand game.
"Gavin's toe problem has also cleared up well, meaning he has been able to train fully and we don't anticipate any recurrence of that particular issue."
With Jones fit to start at fly-half and resume the captaincy, Jenkins would have to decide between Henson and James Hook for the inside centre position.