Defender Sowunmi and midfielder Smith were both shown red cards during Yeovil’s 2-1 home defeat to Crawley on New Year’s Day.
Yeovil boss Darren Way will also be unable to call on James Bailey after the captain was ruled out for up to three months with medial ligament damage.
Barnsley midfielder Jared Bird could make his debut after signing on loan with Yeovil until the end of the season.
Bradford quartet Tyrell Robinson, Adam Thompson, Matthew Kilgallon and Dominic Poleon will all return to the squad.
Left-sided player Robinson and defender Thompson have recovered from illness, while centre-half Kilgallon and forward Poleon both returned to training this week.
Midfielder Jake Reeves is still out due to a recurrence of a pelvic problem, which has forced him to miss the last three matches.
Defender Tony McMahon is doubtful and will be assessed after sustaining a knock in the win at Fleetwood on New Year’s Day.
West Ham United have made an enquiry for Sevilla attacking midfielder Joaquin Correa, reports claim.