With Ryder having gone, they need another batsman, which can only be BJ Watling, who played the last of his five tests against India in Ahmedabad late last year.
Or they could promote wicketkeeper Reece Young to No 6, bump debutant Dean Brownlie to No 5 - his selection having been flagged previously by Wright - with Dan Vettori at No 7 and making room for a fifth specialist bowler.
The bowling options are either to include a second spinner, Jeetan Patel, in a five-strong attack, opt for a two-seam, two-spin option, or go with the more traditional three seamers and one spinner, Vettori, but in one respect it could be a thin attack.
Neither Graeme Aldridge nor Doug Bracewell have played a test. Both, in fact, have made their T20 and ODI debuts on this trip. It's likely Watling will get a start - even against Zimbabwe's lean bowling resources five batsmen sounds a shade skinny.
McKay would be a welcome presence for his lefthanded line offers a point of difference. His only previous test produced one for 120 on a batsman's strip in Nagpur a year ago.
New Zealand have been boosted by the arrival of senior seamer Chris Martin and former captain Vettori.
Martin is sitting on 199 test wickets from 61 matches. The sooner he becomes the fourth New Zealander - after Sir Richard Hadlee, Vettori and Chris Cairns - to 200 the better.
Travelling from Auckland to Zimbabwe for one test is ridiculous, but that's the itinerary that was agreed between the boards.
Tim Southee returns to cricket in the opening round of the Plunket Shield for Northern Districts against Auckland next week. Southee was ruled out of the Zimbabwe test as he recovered from a leg injury.
ZIMBABWE v NZ
Bulawayo, starts 9 tonight:
Zimbabwe (from): Brendon Taylor, Vusi Sibanda, Hamilton Mazakadza, Chamu Chibhabha, Tatenda Taibu, Forster Mutizwa, Malcolm Waller, Elton Chigumbura, Prosper Utseya, Ray Price, Kyle Jarvis, Natsai M'shangwe, Chris Mpofu, Keegan Meth, Njabulo Ncube.
New Zealand (from): Ross Taylor, Brendon McCullum, Martin Guptill, Kane Williamson, BJ Watling, Dean Brownlie, Reece Young, Dan Vettori, Doug Bracewell, Jeetan Patel, Andy McKay, Graeme Aldridge, Chris Martin (two to be omitted).