"It's great to be kind of back," Kane said. "I know I'm not on the ice, but I'm in the same kind of morning routine and I'm hoping, at least initially while I can't do much, I can maybe be around the team as much as I can. So, that will definitely be helpful as the recovery process happens."
Kane had been in nearby Fort Lauderdale awaiting his teammates in advance of their game against the Florida Panthers at FLA Live Arena on Saturday (4 p.m. ET; SN, BSFL, ESPN+, SN NOW). He traveled in a town car Wednesday from Tampa, where he had surgery after being a cut by a skate blade in Edmonton's 3-2 win at the Tampa Bay Lightning on Tuesday.
The Oilers lost 7-2 to the Carolina Hurricanes in Raleigh, North Carolina, on Thursday.
"I know I see a doctor on Wednesday, but other than that, just kind of taking it day by day," Kane said. "Hopefully, things heal and I do everything I can to get things to heal as fast as possible; then, just come back once everything is 100 percent, but I'll try to make that as soon as possible."
Kane, who was placed on long-term injured reserve Wednesday, will travel back to Edmonton with the Oilers after the game Saturday.
"He had a big smile on his face," coach Jay Woodcroft said of Kane after he returned to the team. "I know the fellas were so excited to see him and see that he was OK. Just seeing that he's OK, and then him being around his teammates, put a smile on everybody's face today."
Kane was injured when Lightning forward Pat Maroon accidentally skated over his wrist when Kane was on the ice following a collision with Tampa Bay defenseman Philippe Myers.
"Thank you all for the kind wishes and prayers from over the past several hours," Kane tweeted Wednesday. "Obviously last night was an extremely scary moment for me and I'm still in a little bit of shock. I would like to thank the entire training staff of the Edmonton Oilers and Tampa Bay Lightning, along with all the doctors and paramedics who rushed to help treat and repair my injury. Without all of you, I know things would've been much worse and I'm sincerely grateful. I won't be back next game, but I will be back, and I look forward to being back on the ice playing the game I love alongside my teammates in front of our great fans."
Kane has 13 points (five goals, eight assists) in 14 games this season. He signed a four-year, $20.5 million contract ($5.125 million average annual value) July 13.
"I brought him into the coaches room and we came up with a plan for his work off the ice. He was all excited about that," Woodcroft said. "I think he's got to heal up, but I also think it's an opportunity when he heals up that the rest of his body heals up. It's an opportunity for him to put some good work in too while he gets ready and the hand gets ready."
Edmonton recalled forwards Mattias Janmark and Klim Kostin from Bakersfield of the American Hockey League on Wednesday. Janmark played 10:52 against the Hurricanes in his Oilers debut. Kostin was a healthy scratch.
NHL.com independent correspondent Kurt Dusterberg contributed to this report