The trio is charged with violating royal defamation laws in addition to sedition charges slapped on all 18 activists indicted on Monday over a rally in central Bangkok in September.
Hakeem al Araibi's rejection of extradition means a trial will be held to determine whether Thai authorities will send him to Bahrain, where he fears he is at risk or torture.
Mitsutoki Shigeta, 28, became the centre of a "baby factory" scandal in 2014 after Thai police said DNA samples linked him to nine infants found under the care of 24-hour nannies in a plush Bangkok apartment.
After Yingluck Shinawatra failed to show up at court for a verdict hearing, Thailand's Supreme Court said it will issue an arrest warrant for the former prime minister. Sources close to her say Shinawatra has fled the country.
An army general, two provincial politicians and police officers were among those found guilty in Thailand's biggest human trafficking trial.
Thailand's ousted prime minister Yingluck Shinawatra says she will 'use every channel available to fight' against the order.
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