Australia must also resist the urge to engage hostile Kiwi crowds - prone to throwing missiles at visitors from across the ditch.
"I would say New Zealand crowds are the hardest to play in the world," said Waugh, who enjoyed just four Test wins from 10 matches in New Zealand between 1986-2000.
"They are very personal and if you get goaded into responding you can get distracted. You tread a fine line."
Smith hasn't passed 30 in his last five limited overs hit-outs against New Zealand and India. However Waugh backed Smith's unconventional technique against the moving ball and temperament against canny counterpart Brendon McCullum.
"He has worked out his own game, has a tremendous pair of wrists and plays the ball late, hit gaps," said Waugh of Smith with 1286 Test runs at 71 over the past 12 months.
"He has deficiencies but the great thing about Steve is that when people write him off he scores runs.
"He goes about his business in a quiet, confident manner which people gravitate to. The best leaders don't act, they just do. That's the type of leader he is."
Waugh noted using Smith as a T20 foot soldier with Aaron Finch as captain was misguided. Taking charge for the World Twenty20 in India next month and across all forms is best for all concerned.
"It will be harder for him playing in a T20 game and not being captain," said Waugh, who will front his Waugh in the West charity match at Adelaide's St Clair on Friday to raise funds for children with rare diseases.
"His natural instinct would be to take over, run things and be in the captain's ear.
"If it becomes too much he can let people know but I think it makes sense for Steve to lead in India.
"You can see the players respond to him, know where they stand."
And recently retired Australian wicketkeeper Brad Haddin has also weighed in, writing that Steve Smith and his team must find the "little demons of self-doubt" New Zealand have from past history against Australia.
The veteran wrote a column for espncricinfo suggesting Australia still holds a psychological grip over the Black Caps.
"Despite their recent achievements, I still believe a mental hurdle does exist for New Zealand when it comes to facing Australia, particularly in test matches," he wrote.
"We have always viewed the Ashes as our No 1 goal, and often that has added to the pressure of a series. For the Black Caps, their equivalent is to face Australia, and they would love nothing more than to come out on top.
"As a result, there's a lot of pressure both externally and internally to beat Australia.
"I know from personal experience that we faced numerous New Zealand teams in the past that, deep down, were not sure if they believed they could beat us.
"Under Brendon (McCullum), belief has grown enormously within New Zealand cricket, but those little demons of self-doubt will still be there in some form."
"We talked often about playing teams on skill and not emotion, and it is more relevant than usual over the next couple of weeks.
"The end of the Chappell-Hadlee series in Hamilton showed how much emotion there is around Brendon McCullum's final summer as an international player, and there will be plenty more of that when we come around to his 100th test in Wellington and his last one in Christchurch.
"Therefore it is very important that Australia focus on the right things leading into this series. That means not getting caught up in that emotion, concentrating on the job at hand, and then enjoying a beer with the New Zealand guys at the end of the series.
"The right time to celebrate Brendon's career will be in those closing moments, not before."
-news.com.au
