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England completed a 2-0 series whitewash with a crushing 247-run win in the second Test at Headingley concluded Tuesday - a match where Cook became the first England batsman to score 25 Test hundreds with a second innings 130.
But the teams have now switched formats, with the first of a three-match one-day series taking place at Lord's -- where England won the first Test by 170 runs after New Zealand collapsed to 68 all out - on Friday.
However, when the two sides met in limited overs action in New Zealand earlier this year, the results were much closer.
Now the tourists have also been bolstered by the arrival of several experienced one-day specialists ahead of next month's Champions Trophy tournament in England and Wales featuring the world's top eight teams in 50 overs per side cricket.
"I think it's always been the strength of their cricket, the shorter forms," Cook told reporters at Lord's on Thursday. "Out in New Zealand both the Twenty20 and one-day series went down to the last game, so we are expecting another tight contest.
"New Zealand are a very strong one-day team and their record in big trophies, in big games proves that."
Cook added county experience of playing in different formats would help those players also in the Test squad cope with the change to coloured clothing and two white balls.
"It's obviously a very quick turnaround, seems quite strange after only a day off.
"In county cricket we've been brought up playing a four-day game then almost the next day a one-day game, a Twenty20 game.
"We are all quite used to it. But it's making sure mentally we are right and looking to do the basics well. We have got options, depending on conditions."
This series will effectively act as England's warm-up for the Champions Trophy but Cook insisted it was important in its own right.
"As players we have to look at it a series we want to win. It will be good preparation (for the Champions Trophy) when we get there but we have to look at this series in total isolation."
Thursday saw star batsman Kevin Pietersen having a net with his England colleagues at Lord's before enjoying a solo fielding drill session on the main square as he continued his recovery from a knee injury.
England hope to have Pietersen back fit in time for the first Ashes Test against Australia at Nottingham in July and Cook said: "It's great news for English cricket to have him back practising again. Things are looking good on that front."
