Players also have the opportunity to make the cut for the Hawke Cup campaign from next month as well as the CD A programme.
Schaw's brother and CHB captain, Scott, missed out in the Bay team. Jeremy Kuru and Liam Rukuwai were unavailable due to injury.
Sinclair said he had appointed Smidt captain despite the presence of Stags skipper Kruger van Wyk because he was looking at the Hawke Cup when CD players won't be available.
"With myself, Kruger and Kieran [Noema-Barnett] around Stevie will learn heaps."
He wasn't sure what Black Cap Doug Bracewell's bowling load was likely to be but he would start the Taradale allrounder as a batsman when he returns from training at the Lincoln camp, near Christchurch, this week.
HB team: Stevie Smidt (c), Doug Bracewell, Graeme Tryon, Mathew Sinclair, Ajaz Patel, Andrew Mathieson, Indika Senarathne, Luke Kenworthy, Ben Stoyanoff, Charlie Robson, Kruger van Wyk, Kieran Noema-Barnett, Luke Wright.