The series begins in Colombo on Wednesday but given the wet season in Sri Lanka, weather is expected to play a role throughout - so much so that five reserve days have been provisionally scheduled.
Inclement weather reared its ugly head on Sunday when an England XI clash with Sri Lanka A was abandoned without a ball being bowled.
That means England head into the series with just one warm-up game under their belt - a 56-run win via the Duckworth-Lewis method on Friday.
An England XI chased down a revised target of 90 against Sri Lanka A - set to them in 25 overs - in comfortable fashion and batted their allotted time, finishing at 145-2.
Cook hit 54 from 62 deliveries himself, while Moeen Ali, promoted to the top of the order, impressed with a 37-ball 56.
It was a knock that may see Moeen fill the role as Cook's opening partner - widely expected to be taken by Alex Hales - in the series opener.
Cook was encouraged by the performance and told the England and Wales Cricket Board's official website that he expects big things on the tour.
"We haven't won many series' in the past year and this is a tough place to do it," he said.
"If we get on a roll and play well then you never know. It's a really exciting place to be at the moment.
"It will be a challenge for some of these guys, to play their first England games in sub-continent one-day conditions - it's hard.
"We will get better as the tour goes on. I'm very excited because I think we can do something very special."
Moeen (3-29 off nine overs) and paceman Steven Finn (2-43 off eight) bowled well in the warm-up match.
But Sunday's abandonment meant the likes of Hales, James Taylor, Ravi Bopara and Harry Gurney - all in the squad - are without official match practice before the series.
England last played one-day cricket in August and September against India, a series they lost 3-1.
They also lost a series to Sri Lanka on home soil, 3-2, in May and June, and were defeated in their last one-day international in Colombo.
That match - a quarter-final at the 2011 ICC World Cup - saw England struggle to 229-6, a score Sri Lanka chased without losing a wicket and with more than 10 overs to spare.
The Sri Lanka A team that faced the England XI is likely to bear little resemblance to Angelo Mathews' side for the series opener.
But Mathews' men have some atoning to do, after being thrashed 5-0 in a hastily arranged one-day series in India earlier this month.
Two of the defeats in India were over 150 runs and changes are likely as Sri Lanka go in search of the form that saw them also win in England in the Test and Twenty20 series - as well as their 50-over success - earlier this year.