Other options include playing three seamers and bringing in left arm spinner and useful batsman Mitchell Santner, to complement Mark Craig's offspin.
"Tim is a strong leader within the group. We trust him completely and he'll make a decision which he believes is the best for the team," McCullum said.
He said there were good options in the squad and "whatever happens (with Southee) we are confident we'll take in a team that is going to get the job done."
How New Zealand handle the heat, in more ways than one, will go a long way to determining their prospects of squaring the series.
Temperatures are expected to touch around 36degC over the first two days at least.
Australian are talking about using neckerchiefs with cooling ingredients.
New Zealand's players are used to extreme temperatures in foreign conditions and are sure, with regular hydration, they will be okay, but now add in the heat of Australia's fast bowlers.
The Australians have been talking up the fire in the Waca pitch - in what's expected to be the final test at the old ground -- and their plans to make New Zealand's batsmen sweat.
There's an element of typically Australian trash talk about it, but it is not wholly misplaced.
New Zealand, for all their wayward bowling at the Gabba during the first test loss, simply must bat long in their first innings to make sure they stay in the contest.
In eight of their last 16 first innings, they have passed 400; only three times dropped below 250, so they are not without form in that area.
"We're not surprised by it," New Zealand captain Brendon McCullum said of the Australian chatter.
"The Waca is a fast, good wicket, a fast-scoring ground and if you get through the first 15-20 balls, with the ball potentially hitting the stickers on the bat, then you can develop your cross bat shots and score pretty quickly."
And while that first innings will be critical - seven of the last nine toss winners have batted first at the WACA -- McCullum singled out the bowling in Brisbane as the most disappointing aspect.
"We were just a little bit off," he said.
"It could have been anxiety about such a big series, or we hadn't played for a while; or it could be that they knocked us off our length."
Time, then for new bowling coach Dimitri Mascarenhas to earn his corn.
Maybe it was a bit of everything, but more of the same in Perth and New Zealand will be shunted out of the series before even reaching the pink ball test in Adelaide.
There is fortitude and skill within the New Zealand team. The likes of Kane Williamson, Trent Boult, BJ Watling and McCullum all possess high degrees of talent in their specialist field.
New Zealand simply have to dig deep and back themselves.
Brisbane was poor; Perth cannot afford to be.
