The pair have been named in a relatively inexperienced Volts team missing several leading players, including its star batsman.
Ryder is still struggling with a back injury and it could be some time before he returns for Otago.
''We are still waiting to see how Jesse pulls up after extending training and physio,'' coach Dimitri Mascarenhas said.
''It is not good at the moment. He is not responding as well as he would have liked or we all would have liked. We are actually unsure of a return date at the moment.
''It is a disc problem ... and he is getting shooting pains. He is unable to run at the moment, so until he can run it is going to be tough for him to get back in the team.
Test players Brendon McCullum, Mark Craig, Neil Wagner and Hamish Rutherford all featured in Otago's 82-run Plunket Shield win against Canterbury but will be in Christchurch for the Boxing Day test against Sri Lanka.
All-rounder Jimmy Neesham is permanently absent these days due to his busy international schedule.
But Otago does get one Black Cap back. Offspinner Nathan McCullum returns after helping New Zealand record a 3-2 one-day series win against Pakistan in the UAE recently, and veteran pace bowler James McMillan returns from an knee complaint.
Seamer Tipene Friday has recovered from a back injury but has been overlooked, with Sam Blakely getting his first opportunity this season.
Jacob Duffy and Bradley Scott round out the seam attack.
The captain, Aaron Redmond, will miss the December 30 one-dayer in Queenstown to be with his wife, Katie, for the birth of the couple's second child. His spot will be taken by Ryan Duffy, who will also be making his one-day debut.
McCullum and Sam Wells are likely to bat further up the order to take some pressure of the likes of Rodden, Finnie and Ryan Duffy.
Rodden has played six first-class games and four twenty20 matches for Otago. He scored a first-class hundred in his second match for the province but struggled in the Super Smash.
Finnie, who turned 18 last week, has played two twenty20 games for Otago and is very much still learning his craft.
The all-rounder took two for nine on debut with his off-breaks and looked well equipped with the bat.
Ryan Duffy, Jacob Duffy's elder brother, has played four first-class games, posting a useful 48 in his last knock.
Blakely, a pace bowler, has played just two one-day games, making his debut in March 2013.
At the other end of the spectrum, Redmond (78), Derek de Boorder (62), Scott (59) and McMillan (51) have played 250 one-day games for Otago between them.
OTAGO
The one-day team is.-
Aaron Redmond (captain), Sam Wells, Michael Bracewell, Nathan McCullum, Brad Rodden, Iain Robertson, Derek de Boorder, Josh Finnie, Bradley Scott, Jacob Duffy, James McMillan, Sam Blakely.
