The winners of the group qualify directly for South Africa while the second place side will play off over two legs for another place, provided they are one of the best eight runners-up in the nine European groups.
Switzerland are aiming for their second successive World Cup finals and take a seven-match unbeaten record into the tie, including a 2-1 win in Greece last October.
"We know that the Greeks are strong, they are compact and they are dangerous at set pieces," former Bayern Munich coach Hitzfeld, whose contract was recently extended until 2012, told reporters.
Hitzfeld, already missing Johan Djourou because of injury, must also decide whether or not to risk his Arsenal team mate Philippe Senderos, a regular for his country but who has yet to play for his club this season.
Senderos looked vulnerable and short of practice during the goalless draw at home to Italy last month.
Hitzfeld's worries mounted when central defender Stephane Grichting took a knock in training on Tuesday, a particular concern as Lazio's Stephan Lichtsteiner is suspended.
With Philipp Degen struggling to get a game at Liverpool and Valon Behrami injured, Lichtsteiner is likely to be replaced at right back by Alain Nef, who plays in the Italian second division.
"When in Switzerland, we lose three players for the same position, then we have a problem," said Hitzfeld.
Greece, whose only previous World Cup appearance was in 1994, will be without their influential midfielder Giorgos Karagounis who is injured and is expected to be replaced in the starting line-up by Sotiris Ninis.
Seeking to avenge their only defeat in the group, coach Otto Rehhagel is also likely to field three strikers with in-form Yannis Amanatidis playing just behind Fanis Gekas and Dimitris Salpingidis or Angelos Haristeas.
"We will play to win," said defender Vangelis Moras. "It all depends on our own performance. It is only in our hands."
Fellow striker Giorgos Samaras has been ruled fit to play and could come on as a substitute.
Switzerland - Diego Benaglio; Alain Nef, Steve von Bergen, Stephane Grichting, Ludovic Magnin; Tranquillo Barnetta, Gokhan Inler, Marco Padalino, Gelson Fernandes; Alex Frei, Blaise Nkufo
Greece - Kostas Halkias; Loukas Vyntra, Sotiris Kyrgiakos, Avraam Papadopoulos, Nikos Spyropoulos; Christos Patsatzoglou, Kostas Katsouranis, Sotiris Ninis; Fanis Gekas, Angelos Haristeas, Yannis Amanatidis,
