Speaking to Al Jazeera, he said the NLD officials were hopeful that they would secure a more favourable verdict in a higher court.
The convictions on Tuesday saw Aung San Suu Kyi's house arrest extended for another 18 months, while Yettaw, a Vietnam war veteran who suffers from epilepsy, was sentenced to seven years of hard labour and imprisonment.
Nyan Win said the appeal process could begin immediately once they received a copy of the judgement.
Khin Maung Oo, the lawyer representing Yettaw, said they would also appeal "step-by-step" to the Myanmar court system.
If necessary, he said, he would write to senior officials in Myanmar's military government to ask for Yettaw to be deported.
He said his client was "very calm" and "hopes for the best".
In Tuesday's sentencing, judges originally sentenced Aung San Suu Kyi to three years of hard labour and imprisonment.
But that sentence was immediately commuted on the orders of Senior General Than Shwe, head of Myanmar's military government, to 18 months house arrest.
In a statement Than Shwe Than said he had reduced the sentence to "maintain peace and tranquillity and because Aung San Suu Kyi was the daughter of Aung San, a revered hero who won Myanmar's independence from Britain.
During the trial Aung San Suu Kyi's lawyers had argued that the law used to charge her was invalid because it applied to a constitution abolished two decades ago.
They also said that government guards stationed outside Aung San Suu Kyi's compound should be held responsible for any intrusion in her property.