Probably nothing would happen.
Below is the passage in which Snape accepts the three “terms” of the Unbreakable Vow to protect Draco. Notice how there's a “tongue of flame” for each term of the Vow. This tongue seems to be magically binding Snape to the Vow, and he seems to be accepting each part separately: at least, he’s bound by it before being asked about the other parts. Were he to decline one part of the Vow, his declaration to uphold the other two parts wouldn’t be affected.
Here we go:
Narcissa spoke.
“Will you, Severus, watch over my son Draco as he attempts to fulfil the Dark Lord’s wishes?”
“I will,” said Snape.
A thin tongue of brilliant flame issued from the wand and wound its way around their hands like a red-hot wire.
“And will you, to the best of your ability, protect him from harm?”
“I will,” said Snape.
A second tongue of flame shot from the wand and interlinked with the first, making a fine, glowing chain.
“And, should it prove necessary… if it seems Draco will fail…” whispered Narcissa (Snape’s hand twitched within hers, but he did not draw away), “will you carry out the deed that the Dark Lord has ordered Draco to perform?”
There was a moment’s silence. Bellatrix watched, her wand upon their clasped hands, her eyes wide.
“I will,” said Snape.
Bellatrix’s astounded face glowed red in the blaze of a third tongue of flame, which shot from the wand, twisted with the others and bound itself thickly around their clasped hands, like a rope, like a fiery snake.
— Half-Blood Prince, chapter 2 (Spinner’s End)
IANAML (I Am Not A Magical Lawyer), but it certainly reads like three separate Vows. Ergo, accepting or declining any part would have no effect on the others.