While today's training session was not a crucial one in terms of the side's general preparations - it is optional and indoors because of rain in Wellington - the potential loss of Williamson would've been a big blow for the Black Caps.
Williamson scored 251, his third double century in test cricket, as part of a winning performance by the Black Caps in the first match of the West Indies series and looks in ever-fine form ahead of tours against Pakistan and Australia over the remainder of the summer.
Despite the potential disruption caused by his absence, Stead said a contingency plan is in place for what would be a milestone event in Williamson's life.
"Worst case scenario Kane misses some matches," Stead told media on Monday. "As a dad, as a parent, you only get that opportunity once in your life to be there for your (first) child's birth and I know that it's important for Kane too.
"At the end of the day we play cricket and other things are much more important."
"It's a very exciting time in anybody's life and it certainly is in mine," said Williamson of impending fatherhood.
Should Williamson miss time, Stead has indicated that Will Young, who made his test debut last week, was the "natural replacement" for the skipper.
Meanwhile, the Black Caps received more good news in the form of the full recover of BJ Watling from a hamstring injury and will return to the side.
Tom Blundell will open the batting order with Tom Latham and Will Young will drop out of the starting XI - barring Williamson's absence. A decision on which all-rounder - Darryl Mitchell or Mitchell Santner - will make the starting team will be made tomorrow morning.
The second test is scheduled to begin on Friday at 11am at the Basin Reserve where today's rain is forecast to clear for the full five days of play.