Cook's tourists on Sunday will begin a three-match series at Seddon Park which will be England's last before they have to name their 15 to take part in June's mini-World Cup on home soil. England have yet to win a 50-over global tournament, and were eliminated in the initial stages the last time they tried to do so at home - 14 years ago.
The stakes are therefore perhaps higher than normal for an ODI series in New Zealand, especially for emerging or fringe players, and Cook said: "It's the last three games before we announce the ICC Champions Trophy squad - which will be about a month before we play it. So this is the last three games for anybody to put their hand up for selection."
England have obvious credentials for a successful campaign when the world arrives on their doorstep in June.
Cook is encouraged by their form under his captaincy over the last two years, and last month's 3-2 defeat in India - new limited-overs coach Ashley Giles' first in charge - was an improvement on two previous 5-0 whitewashes in that country.
Giles' appointment, however, to replace Andy Flower and allow the latter to concentrate on Test matches, puts England in a transitional phase.
"Clearly, it changed the balance a little bit when Ashley Giles took over as coach only in January," said Cook. "We were very settled with Andy Flower. So things have changed a little bit there, with the change in management.
"But we're (still) a very settled squad in one-day cricket, and have been playing very well for quite a long period of time now."
The return of three first-choice players - Graeme Swann, James Anderson and Jonathan Trott - after being rested for India also means some tough decisions will have to be taken about who makes way.
"We do have slight selection headaches," added Cook. "But as coach and captain, that's what you want and need to produce a good squad."
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