The first of the two-match series begins at Lord's on Thursday and the tourists have just one selection decision to make before the toss.
Martin played all three drawn games against England in New Zealand earlier this year, but with unsettled conditions in London the Black Caps are pondering an all-seam attack.
That brings Bracewell back into the equation after a spell out of the XI that initially started when he cut his foot while cleaning up after a get together at his house.
Bracewell had been hoping to nudge ahead of Neil Wagner in the pecking order, but he has performed strongly in the tourists' warm-up fixtures.
"Wagner definitely plays," McCullum said. "It's either Martin or Bracewell for the last position, otherwise it's the same team from back home.
"It's just a balance issue of trying to work out whether to play the four seamers or use the same set-up as the three Tests back home.
"That's something we have to look at in the morning before making a call.
"Overhead conditions are something we have to be aware of and we have to take into the account the forecast too. If the game does get shortened (by rain) you look at how that impacts on the spinner's ability to impose himself on the game.
"I don't think we'll lose much either way, it's just a slight tweak of the balance."
- Sports & Recreation