In the movie when Harry tries to shake Quirrell's hand he doesn't cuz he knows that Harry's touch would make him disentegrate. However, in the book, Quirrell does shake hands with Harry. But how is this possible?

harry did shake hands with quirrel in leaky cauldron. But quirrel wasn't trying to kill Harry that day, so harry didn't need the protection fron his mother. In the end of the book quirrel tried to kill harry with his wand, harry touched him and it burned his skin.

perhaps he was wearing a glove

yea i thought about that too

if tu pay más attention to hte scene, when Harry meets Quirrel in Londres - you'll notice, that Harry wanted to shake professor's hand, but Quirrel didn't respond

they never shook hands bc quirrel knew that he would get killed