Johnson is expected to go three innings or throw 55 pitches, "somewhere in there," said manager Buck Showalter. Wada threw his second bullpen session yesterday and could go two innings on Saturday.
Johnson is on the 15-day disabled list with a strained right lat. Wada underwent ligament-reconstructive surgery on his left elbow in May.
Dylan Bundy, on the seven-day minor league disabled list with right elbow discomfort, will start a throwing program on Thursday.
Showalter said it was difficult saying goodbye to reliever Luis Ayala, traded today to the Atlanta Braves for Double-A left-hander Chris Jones.
"Yeah, it was," Showalter said. "Luis will like it there. Atlanta is a good spot for him. It's a good club. But we like the player we got back. We like the conventional 12 pitchers and get our bench back at full strength and also create some opportunities. Kind of knowing who we are, and wanting to take a look at T.J. (McFarland) and some other people, we feel like we have some depth to withstand it if there's an issue. It's something we've been thinking about."
Showalter listed the reasons why the Orioles chose Dickerson.
"Plus defender, plus-thrower. A left-handed bat. The guy has had experience in the American League East," Showalter said. "And at this point, as we wait on Wilson (Betemit) and Brian (Roberts) to come back to us, we've got options. He's one of many we think can help us here.
"You can see why he's been coveted by people. Always a little question why he hasn't at 30, 31... There's not much there not to like. He played his butt off all spring. He competed. And he knows the gig. He knows what's expected here. I was really impressed with him defensively and running the bases."
Showalter didn't intend to play with a three-man bench for long.
"Dan (Duquette) and I knew it wasn't something we wanted to do very long," he said. "We were on the same page. We had to wait until we could get the right player back and the right deal where Luis was concerned. We'll see. We got a 23-year-old left-handed pitcher (McFarland). He's going to have to have some success in order to keep him. We can't just carry some guy. But we like him.
"It wasn't completely about keeping T.J. We like the player we got back. We knew we weren't going to be at 13 pitchers all year. After the off day, we felt it was gong to be a good time to go.
"If there's an adjustment that needs to be made, we'll make it. We can go back to three position players very easily and we can do it out of our bullpen if we have to. Our maneuverability is still the same as it was. Obviously, Luis didn't give us any maneuverability."
Nolan Reimold is back in the lineup as the designated hitter after experiencing tightness in his right hamstring, and could play in the field if Showalter chose to put him out there.
"I think if you're comfortable with him DHing, you're comfortable with him playing the field," Showalter said. "All indications are he's fine and ready to go. But until you get in the game, you never know. He says he feels good. It was something he had early in the spring, but it went away and it kind of showed its head again that last time down the line. But he said he feels good now."