However he's very much in the selectors' minds for the world T20 in Bangladesh, starting in mid-March. These two games against the West Indies are New Zealand's last warmups for that and so it's a case of priority selections.
Selectors Mike Hesson and Edgar wanted to give Central Districts speedster Adam Milne a chance.
"We are well aware of Kyle's skills at this level," Edgar said. "We would like to give Adam an opportunity and he hasn't had that with the weather [during the West Indies ODI series].
"We are trying to see players perform at the highest level and give them a chance."
It's a different story with Williamson, a classy batsmen if more of an accumulator than a regular boundary clearer, anda useful offspinner and fine fielder.
He's played 13 T20s, averaging 22 with the bat but taken only two wickets. To be fair, he's been given a bowl in only four games.
Williamson might still go to Bangladesh in March, where the slower pitches demand players who are adept both against spin and at delivering it. For now, his card has been marked as a test and ODI priority player.
"That's probably where we see him at the moment," Edgar said. "He's playing so well in that. Dropping down to an even shorter version, we're less inclined to involve him there."
Edgar admitted that there was a measure of urgency about the next two T20s.
"These guys [in the 12] will be treating it with absolute urgency. They know a World Cup is coming up and they'll want to be part of it. For us, picking sides is still pretty much performance driven.
"You think of Anton Devcich, or a Tom Latham or a Hamish Rutherford. These guys are in and around, knocking on the door. It's quite a good position to be in."
The New Zealand 12 is the same as for the ODI series, minus Mills and Williamson, a nod to the selectors' thinking that there's no need for major tinkering between the two short-form formats.
"The ODI team is going along pretty well and there are some good signs and performances coming through there," said Edgar. "We just want to make sure they continue with that. These guys have the ability to carry that on with the T20 as well."
An initial squad of 30 players for the world T20 will be announced on January 16, as per International Cricket Council requirements, before being trimmed closer to the tournament.
T20 squads
New Zealand: Brendon McCullum (c), Jesse Ryder, Martin Guptill, Ross Taylor, Corey Anderson, Colin Munro, Luke Ronchi, Nathan McCullum, Jimmy Neesham, Tim Southee, Mitchell McClenaghan, Adam Milne.
West Indies: Dwayne Bravo (c), Kieran Powell, Johnson Charles, Lendl Simmons, Andre Fletcher, Narsingh Deonarine, Denesh Ramdin, Chadwick Walton, Jason Holder, Samuel Badree, Tino Best, Nikita Miller, Sunil Narine, Ravi Rampaul, Andre Russell.
Schedule
Sat: 1st T20, Eden Park
Wed: 2nd T20, Wellington