The match, which will still take place at the home of Hednesford Town, will now kick-off at 12noon, rather than 7pm as originally scheduled.
The Baggies game will be the second time the two sides face each other in six days, with a home encounter in the Central League Cup preceding this fixture.
It will be the Russ Wilcox's side's third of six Premier League Cup Group Stage matches, having already faced West Brom and Newcastle United at the Sands Venue Stadium.