An ankle injury sustained in the defeat to South Africa has left Umaga a doubt for the match and Henry has named his Wellington colleague Conrad Smith as an option in case the skipper fails to make it.
But Umaga's chances of featuring in Sydney improved after a smooth intercontinental flight.
He was upgraded from business to first class for the 12-hour trip from Johannesburg, and was able to ice his ankle for the duration.
"It's day by day at the moment, but I'm pretty positive about injuries, as I always am," Umaga said.
"I'd like to be running by Thursday. It gives me and the team an indication of where I am and whether or not I'm going to be available."
Henry has made two definite changes from the side defeated by the unbeaten Springboks.
Half-back Byron Kelleher's injury-forced omission is confirmed, with Piri Weepu taking the number nine shirt.
Joe Rokocoko replaces Leon MacDonald, with the Aucklander starting on his favoured left wing ahead of Sitiveni Sivivatu.
Mils Muliaina reverts to full-back, while Bay of Plenty's Kevin Senio will make his Test debut should he get game time off the bench.
New Zealand: M Muliaina; R Gear, T Umaga (captain)/C Smith, A Mauger, J Rokocoko; D Carter, P Weepu; T Woodcock, K Mealamu, C Hayman, C Jack, A Williams, J Collins, R McCaw, R So'oialo.
Replacements: D Witcombe, G Somerville, J Ryan, M Holah, K Senio, L McAlister, L MacDonald.