The translation is not wrong.
The key of your question is 「しか」 and "only".
The usage of 「しか」 combined with negatives (here, 「ない」 in 「奪えない」) translates into "only".
Here, as 「奪えない」 is 「奪える」 plus 「ない」, 「あなたからしか警察はノートを奪えない」 is equivalent to something like 「警察はノートを奪える only あなたから」.
So its translation would be "police can recover the Death Note only from you," which is equivalent to the original translation.
「これなら」 is translated to "Now" in your sentence and has nothing to do with your question.
The literal interpretation of 「これなら」 is "if this"; or "if the situation is like this".
In this context the situation is already determined to "this", so the interpretation is more like "Now that the situation is like this", which is condensed into "Now" in your sentence.