Snape could be quite shocked. Given their history, he never expected such a gesture from Harry. He may be at a loss for words for a moment, and then start to think about how to use the basilisk parts to his advantage, all the while still maintaining his usual sullen exterior.
He might be initially suspicious. Snape is a cautious man, and he may think that Harry has some ulterior motive, like setting him up. But after realizing Harry's sincerity, he could be grudgingly grateful.
Snape might immediately see the potential of the basilisk parts. He is a potions master and very knowledgeable about dark creatures. So, he could start formulating plans in his head right away, while still being a bit flustered by Harry's unexpected kindness. He might try to hide his true feelings, but his actions would show his eagerness to use the parts for something important.