Taylor had throw downs in the nets yesterday (Monday) and Wright was hopeful he might play the final one-dayer and Doug Bracewell (back) and Andrew Ellis (leg) were both progressing well.
The test players - Kruger van Wyk, Neil Wagner, Daniel Vettori and Chris Martin - also arrive in the West Indies this week but won't be pitched into battle. They will briefly stay in St Kitts to acclimatise before heading to Antigua ahead of the three-day warm-up match and two tests.
It puts enormous pressure on McCullum to help turn things around.
New Zealand have been well beaten in all four games and their lack of preparation has been evident. In contrast, the West Indies are battle-hardened after playing Australia and England.
Wright said his side hadn't been good enough and pinpointed hard-hitting opener Chris Gayle as the important wicket to pick up tomorrow.
He recently ended a long-running dispute with the West Indies board and has plundered scores of 63 not out and 125 in the opening two 50-over affairs, while he also posted consecutive 50s in the Twenty20 games.
Wright was looking at using Northern Districts paceman Trent Boult, who joined the New Zealand side following their injury woes, in a bid to dislodge Gayle and said they also needed to decide whether to play two spinners.
"It's a very flat wicket, an even smaller ground straight than Jamaica, so we have to do something about our bowling," Wright said. "We think the variation Boult will provide early on in the innings to Gayle [could help] ... We need to do something differently.
"He's put us under pressure right from the word go in the Twenty20s in Miami. It has allowed batsmen to bat around him.
"He's going to fail some time. I just feel if we can bowl better and do things 10 per cent better right throughout our game we will have the opportunity to beat this side with Gayle scoring runs or not.
"It's been challenging to come up to speed but if we can do some thing correctly in this match we are going to get some results somewhere along the line."
Follow Daniel Richardson on Twitter