The problem, as anubhava points out, is that JavaScript doesn't support lookbehind assertions. Sad but true. The lookbehind assertion in your original regex is (?<!\"). Specifically, it's looking only for strings that don't start with a double quotation mark.
However, all is not lost. There are some tricks you can use to achieve the same result as a lookbehind. In this case, the lookbehind is there only to prevent the character prior to the tilde from being replaced as well. We can accomplish this in JavaScript by matching the character anyway, but then including it in the replacement:
input = input.replace( /([^"])~[\d.]*|\?|\*/g, '$1' );
Note that for the alternations \? and \*, there will be no groups, so $1 will evaluate to the empty string, so it doesn't hurt to include it in the replacement.
NOTE: this is not 100% equivalent to the original regular expression. In particular, lookaround assertions (like the lookbehind above) also prevent the input stream from being consumed, which can sometimes be very helpful when matching things that are right next to each other. However, in this case, I can't think of a way that that would be a problem. To make a completely equivalent regex would be more difficult, but I believe this meets the need of the original regex.
