The two countries were placed in Group E with Congo Brazzaville and Uganda when 20 nations were split into five groups this weekend, with the winners going to the finals in Russia.
"I know what Ghana did to Egypt, but that is history," insisted Argentine Cuper, the former manager of Valencia and Inter Milan.
"We fear no team, our target is qualification for the 2018 World Cup, and what lies ahead for the Egyptian squad is work, work and more work."
Ghana Football Association president Kwesi Nyantakyi believes the unexpectedly big winning margin achieved by the Black Stars at home three years ago will work against them this time.
"That triumph does not give us any psychological advantage," he stressed.
"On the contrary, it is a disadvantage.
"Egypt are thirsting for revenge and we must be aware that they have built a new, very good team since Kumasi."
Uganda coach Milutin "Micho" Sredojevic says that although his team are seeded last in the group, they can match Ghana, Egypt and Congo.
"We can create shocks even though our budget is probably 10 percent of some rivals," said the Serb, who has worked in numerous African countries.
"While some other African countries liken us to a motorcycle competing in a Formula One race, I disagree. We can match any team."
Congo coach Pierre Lechantre is not pessimistic either, although Ghana and Egypt seem easily the strongest sides in the group.
"We will face very strong teams, but Congo have a chance," said the Frenchman, who guided Cameroon to the 2000 Africa Cup of Nations title.
The Group C opponents of Morocco coach Herve Renard include Ivory Coast, the country he steered to the 2015 Cup of Nations title, Mali and Gabon.
"All the groups are tough," he said. "You can sense being in a good position, but always have to be careful."
But South Africa coach Ephraim "Shakes" Mashaba says: "I am confident we will be in Russia. The draw made me very happy, although it is not going to be easy."
"We have to start very well," he said, conscious that a draw against Gambia and a loss to Mauritania in Cup of Nations qualifiers means they will not be part of the 2017 tournament in Gabon.
Group A comprises Tunisia, the Democratic Republic of Congo, Guinea and Libya and a blockbuster Group B includes Algeria, Nigeria, Cameroon and Zambia.