Swansea City midfielder Ki underwent surgery for a knee injury he sustained in the 3-2 defeat away to Qatar in June and is not expected to be fit again until mid-September.
That would rule him out of the home game against Iran on Aug. 31 and the final away game against Uzbekistan on Sept. 5.
But Shin, who replaced the sacked Uli Stielike, said he wanted Ki in his squad, regardless.
"I want to give Ki the captain's armband even if he can't play," South Korean news agency Yonhap quoted Shin as saying.
"Ki has been serving a central role well in the national team."
Son broke his arm, also in the Qatar match, but is a better chance to be ready for the Iran game as South Korea look to clinch the second automatic berth in Group A of Asian qualifying and secure a ticket to next year's finals in Russia.
"I think Son has recovered enough to play the World Cup qualifiers," Shin said of the Tottenham striker. "He will not have a big problem.
"I can't call up Son early, but once he returns to South Korea we will check up on his condition.
"Then I have to think about whether I should start him or use him as a substitute."
South Korea are second in Group A, seven points behind the already qualified Iran but only one point above third-placed Uzbekistan who next play China away.
Third place would offer a passage to Russia via a playoff against the third-placed team in Group B and another playoff against a team from the North American, Central American and Caribbean regional qualifying.
Although laden with some of Asia's finest players, the South Koreans' campaign has been far from smooth sailing, with the Qatar loss the final nail for Stielike.
Former captain and Manchester United midfielder Park Ji-sung said the team needed to find the unity lacking under Stielike to push through to Russia.
"The most important thing is that the players must trust each other," Park told local media.
(Reporting by Ian Ransom in Melbourne; Editing by Greg Stutchbury)
