Mark Teixeira’s slow road back to the field continued when he was cleared to take his first two-handed swings Tuesday, albeit underwater, which is less stressful. Wednesday, Teixeira moved on to dry swings (without contacting a ball) as he holds out hope he will be back in the Yankees lineup by early May — and avoid surgery — after suffering a strained tendon sheath in his right wrist while preparing for the World Baseball Classic in early March. “I swung very light [Tuesday] and it’ll just be slow-moving,” Teixeira said before the Yankees’ 4-3 come-from-behind win over the Diamondbacks last night at Yankee Stadium. “Hopefully, it just feels good every day and we’ll see where I am in a week or so on the next road trip.” Teixeira intends to travel with the team to Toronto and then Tampa Bay. If he doesn’t suffer any setbacks, he will remain at the team’s minor league complex in Tampa to rehab. “That’s where we’ll really start ramping up the game speed-type playing,” said Teixeira, who had been limited to one-handed swinging until Tuesday. Though Teixeira said he is optimistic about how his recovery is going, there are considerable hurdles he still has to clear. “I got hurt swinging left-handed, so that’s kind of what I’m worried about,” said Teixeira, who suffered the injury on a check swing. “I’m sure if I play a week of [rehab] games, there’s probably going to be a check swing in there somewhere.” Next up would be hitting off a tee; then soft-toss would lead to batting practice in the cage. Barring any issues, Teixeira would then take batting practice outside for at least a few days before beginning to play in games. “We said 8-10 weeks and I still want to be back in eight,” Teixeira said. “If it has to be a little bit slower because of soreness or tightness, then we can take a little bit more time.” So far, Teixeira said he hasn’t experienced any discomfort.