New Zealand are underdogs for the encounter in Lima after Saturday's first leg in Wellington ended in a goalless draw.
Hudson, however, said his team were used to playing away and ready to thwart Peru's attempt to reach the finals for the first time since 1982.
"We are more comfortable playing away from home and we are more than up for it," Hudson told reporters.
"There is no pressure on us, we have a team full of confidence and a plan. We are a small but strong side and more than anything we believe in ourselves. We're very excited about tomorrow."
"I expect Peru to play very fast to try and get an early goal. The longer the score remains at 0-0 the more the pressure on them will increase," Hudson added in comments made mostly in Spanish.
"Everybody knows that Peru are the favourites. But we also know that if Peru lose it will be a national disaster."
New Zealand expect to have striker Chris Wood back in the starting lineup after injury limited him to a late substitute appearance in Wellington.
"He's good, obviously every day he gets better," Hudson said. "Now we have a Chris Wood who is stronger and more ready."
The winner of Wednesday's intercontinental playoff will join 31 other teams in Russia next year.
(Reporting by Teresa Cespedes; Writing by Andrew Downie; Editing by Toby Davis)
