"It's [about] working through those warm-up games to get as much out of it as I can - personally and as a team - without sort of bothering too much," Williamson said on Wednesday before the team's departure for India. "There is a strong desire to basically be involved in those as much as I can; we've got two of them before our first competition game. And basically it's just wanting to progress [with] what I am doing now - the running, the fielding, and also time in the middle with the bat.

"The load is going to keep increasing, so there is a little bit of an unknown. But it has felt pretty good really in the last few weeks, [I'm] hoping it continues to feel like that. But we're definitely looking to touch on more stuff, [and] introducing myself into the game mode, which is something which we haven't had the opportunity to do."

Williamson highlighted that he still felt certain difficulties as he races against time to be fit to play England in the World Cup opening game in Ahmedabad on October 5. But before that, New Zealand face Pakistan on September 29, and South Africa on October 2 in their two warm-up fixtures.

"Not so much the sprinting; more the slowing actually," Williamson said of the challenges in recovery. "From sprinting to braking, and a little bit of change of direction. But it's all been part of the plan, introducing it towards the end of the recovery. Having said that, there's still obviously time to go with the overall part of it, and keep trying to bank on good days because the rule's pretty much helpful in terms of just moving forward with it."

The injury has also forced Williamson to consider his fielding position and he has all but ruled out fielding at slip.

"We will definitely consider some of that," he said. "Where I field is usually at mid-off, which will probably remain the case. Probably slightly better suited to it than square of the wicket. Potentially some slip, but I won't be standing there if we don't require one."

Southee will be 'ready around first or second game' - Stead

"Tim's seen a hand specialist yesterday, and the key thing for him is really making sure the wound heals. We're still really hopeful that he'll be available early on in the tournament for selection," Stead said. "He's had five pins put in his thumb... He's comfortable, and he'll be ready somewhere around that first or second game.

"So, it's all gone really well. He's had a check in with the surgeon and a hand therapist. They think there might be a little bit of pain still, but he's a tough and resilient character. So we are fortunate to have him with our squad still."

New Zealand have brought in fast bowler Kyle Jamieson as cover and since he hasn't been officially added to the squad of 15, he will not be available to take part in any of the warm-up matches.

"Tim hasn't been ruled out of the tournament," Stead said. "The rules state that you can only get 15 players in your squad, so we've kept Kyle there as cover right now. And that's really just to make sure that if another bowler goes down right before the first game - or if Tim doesn't heal as quickly. If there's some sort of setback, then we have someone there as a ready replacement."