An interesting question. I went back and re-read the passage. Firstly, I should say that my view is that a story does not need to explain every detail – in fact, shouldn't, for it will distract and slow things down. Stories are meant to be read and enjoyed and logic flaws are only bad if they are extremely obvious when reading for enjoyment. Analysing afterwards and discovering plot holes does not detract from the quality of the literature imo. So, this is how I would explain what might have happened:
Offstage, Wormtail crouches waiting. Beside him on the ground lie Voldemort's wand, a robe, and Voldemort's embryonic form. When he hears Harry and Cedric arrive he bundles up Voldemort in the robe, picks up the wand, then moves forward to deal with Harry.
As soon as Harry sees them, his scar hurts so badly he collapses blindly.
Voldemort commands Wormtail to kill Cedric. With Voldemort's wand still in his hand, he does so, then pushes the wand into the bundled robe pocket and lays the bundle down on the ground.
Wormtail now comes forward and uses his own wand to light a wandlight, secure Harry, light the cauldron fire, summon the bone, etc. He drops the naked embryo into the cauldron.
When Voldemort arises fully-formed but naked, he commands Wormtail to robe him, which Wormtail does with the robe from the ground. Voldemort then pulls the wand from the pocket.
At the end of the scene when the spells come out of the wand in reverse order, I believe some minor spells are not directly mentioned such as throwing Wormtail against the tomb, Crucio's etc - though there are several screams from the wand. Then the metal hand he made for Wormtail comes out first, more screams, and so on back to Cedric's death cast by Wormtail, etc.