"I'm a little sore today, but we'll see how it feels," Oswalt said. "I haven't thrown yet. It feels a little better than I thought it would be."
Oswalt will be reexamined in two days to see how he is healing, and said he expects his next start to be pushed back by a day or two, at most.
The right-hander, who allowed one run on six hits in six innings Monday night, is scheduled to start Saturday in Atlanta.
"Hopefully he'll be able to go again on Saturday," Cooper said. "If that's the case, I'm tickled. But we'll kind of monitor that as he goes through the week. Any time a guy starts messing around in that area, it could be the oblique or something else down in that side. He's got to torque, he's got to throw, and that could be a tough injury. I'm glad to know that it's not too bad."
Cooper said if Oswalt is unable start, he could try to stretch reliever Chris Sampson, who started 10 games for Houston, to five innings.
Cooper could also use Oscar Villarreal or Tim Byrdak for extended innings. Jack Cassel, who started two games before he was sent to Round Rock, could possibly come up as well.
"He's our tribe leader," Cooper said of Oswalt. "Hopefully we'd have some guys that would step up, but it would be devastating to lose him for an extended period of time.
We're not going to cross that bridge until later in the week. Maybe by Thursday or Friday we'll have a decision."
Closer Jose Valverde also had an injury scare Monday night. He took a line drive off the back of his throwing hand hit by the Dodgers' Angel Berroa in the ninth.
Valverde said his ring and pinky fingers, which absorbed most of the blow, were not even sore Tuesday morning.
Krysten Oliphant is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.