The tourists have been badly hit by the race selection row while left-arm spinner Robin Peterson has delayed his arrival due to personal reasons. The three-Test series starts on Wednesday.
"We will play one spinner, Paul Harris, and three seamers," said Smith. "I believe we have the team to do the job for us."
He reiterated that the tourists had put behind them the race row controversy which kept leading bowlers, Andre Nel and Charl Langeveldt, out of the tour.
"Once we got on the plane and came here, we got focused on the task at hand," Smith said.
"The boys have been very mature about the whole thing and know that in the end, they will be judged by the cricket they play over the three Tests.
"That is what we are focused on completely."
Nel was omitted from the 14-man squad to fulfil Cricket South Africa's quota of six non-white players in the touring party.
Langeveldt, one of the beneficiaries of that policy, withdrew in protest at being selected on the basis of his colour.
But despite the controversy and depleted squad, Smith said his players were ready to face "one of the most experienced teams in the world."
The Proteas, who took over as the world's top one-day team this month, will clinch the number two Test spot behind Australia if they win the series.
"We are motivated to do well in India," said Smith, who is seeking a hat-trick of South Asian Test successes after winning 1-0 in Pakistan in October and 2-0 in Bangladesh last month.
South Africa have a 3-3 record on Indian soil, including a 2-0 sweep by Hansie Cronje's tourists in 2000, a result that prompted star batsman Sachin Tendulkar to resign as India's captain.
But India go into the series on the back of an impressive tour of Australia, where they narrowly lost the Test series 2-1 and defeated the hosts 2-0 in the one-day finals.
Smith said his main worry was the oppressive hot and humid weather, saying it could have a bearing on the match.
On-field temperatures of around 38 degrees celcius in this southern Indian city, combined with stifling 90 percent humidity, will test both teams over the next five days.
"The heat will affect both teams and I am pretty certain it will be a factor. Whichever team manages the heat better will gain the upper hand," he said.
The Proteas had three days to acclimatise to the heat since their arrival last Saturday, spending long hours in the nets in the absence of any practice match.
Smith and Neil McKenzie, who compiled a world record opening stand of 415 in Bangladesh, lead the Proteas' batting which includes the classy Jacques Kallis and the talented young duo of A.B. de Villiers and Hashim Amla.
Fiery fast bowler Dale Steyn, who has claimed 63 wickets in his last nine Test matches, Makhaya Ntini and Morne Morkel comprise one of the most potent new-ball attacks in modern cricket.
Probable South Africa XI:
Graeme Smith (capt), Neil McKenzie, Jacques Kallis, Hashim Amla, A.B. de Villiers, Ashwell Prince, Mark Boucher, Morne Morkel, Makhaya Ntini, Dale Steyn, Paul Harris.