There appear to be two ways to handle hex codes -- one is the one that you are using:
\x1B
The other is the method used by Mr. Muskrat:
\x{263a}
If you're using 'wide' hex digits (as I assume is the case since you're talking about four digits in this example) then you probably need to use the \x{...} approach.
If you'll tell us a little more about what you're doing, we might be able to move beyond a single substitution. Unless that's all you need, in which case this appears to work:
s/\x{0024}/$delimiter/
And you don't need to make it part of a character class |