I thought about this, too, but there are several problems.
One, like you said, Cap would have access to an axe, but getting the knife would be difficult. Had he used an axe to kill them, the scene would have been way different. Every time Junpei chooses Door 4, Ace picks up the pocket knife from Mr. 9's corpse. Cap somehow getting the pocket knife from a giant who is more than willing to kill him at a moment's notice while he's in a drug addled state seems...unlikely.
Second, everyone would be on guard with someone they've never seen before. He would have been wearing the Zero bracelet, Santa and June would have immediately known who he was, Ace wouldn't be able to tell but would be able to see the bracelet, and Clover would have thought Cap killed her brother. He would have had to have gotten the drop on at least three of them and killed them in quick succession, something that seems unlikely when he didn't even have the knife. Ace could quickly kill Santa and Clover before June noticed, a fifth person coming in and quickly killing three others and going after June doesn't make sense.
Third, June fled through the Jupiter (?) door and the killer followed behind her. The killer stabbed her, but she had not been bleeding for long when Junpei found her. Junpei, Lotus, and Seven followed an empty hallway through the Jupiter door to the submarine. Lotus and Seven waited outside the room June had been stabbed. So let's map this out here:
Grand staircase -|Jupiter|----Hallway----Room Before Sub|Dead June Room
Let's say Cap did it. He started at the Grand Staircase and killed three people quickly, then he chased June through the Jupiter door (again, not sure it was that symbol, but bear with me), through the empty hallway, through the room, in to the Submarine room where he stabbed her. Then, Junpei and crew follow the exact same path with no evidence of blood trails or anything and find June in the final room. After a few minutes with June, Junpei returns to the room outside where Lotus and Seven had been stabbed.
So assuming it was Cap, where could he have hidden? He couldn't have been in the sub room and left there to stab Lotus and Seven because Junpei would have noticed. They would have seen him in the grand staircase because, among other things, he had no reason to think another group was coming and there was nowhere there to hide.
Now, assuming Ace did it, he had the one place you could hide and commit these murders: in plain sight. He stabbed Santa and Clover, chased June to the Sub room, stabbed her, then faked his death on the grand staircase. After which, he stabbed Lotus and Seven by following them through the hallway, waited for Junpei in his addled state after being Seven and Lotus dead, and stabbed him above the sub.
There's also the fact that, if no one went through Cap's room, his doors were still locked since no one opened the pocketwatch door and no one opened the Base Ten door. If someone did go through his room, it would be in Ace's path, and Ace would have killed him.
