A vector is just a length in some particular direction, right? Otherwise how would someone working in your software environment produce the "perfect" reflection vector without knowing the hitting point?
So you should not care where the hitting point is. Just assume the ray is reflected at the origin. Make a vector of length $1$ in the direction of the "perfect" reflection. There is a unique point displaced from the origin by that vector. Use that point as the center of your disk.
The random vector you get in this fashion will be exactly parallel to (and the same length as) the vector you would have gotten by taking a vector from the actual hitting point to a point displaced $1$ unit along the perfect reflection vector from that hitting point and making a disk around that displaced point. That is, it will be the same vector.