This doesn't even take in to account the fact that the Sims 3 is an extremely high-end game. If it's old enough to not have a DVD drive, are you sure that it even has the minimum specs to run the game even if you could do what you wanted to?
But PJSim is correct: if it does meet the specs, digital download is your best bet. From what I understand you can use the keys from your original DVD software to receive a digital download of the game, which won't require the use of discs at all.