A point charge $q$ is at the center of an uncharged conducting spherical shell of finite thickness, with inner and outer radii a and b respectively. Find the work done on the system when $q$ is removed from its original position to a very large distance from the conducting shell, through a small hole in it.

My attempt:

Idea was to calculate the energy of the initial configuration and that would be the work required. Trying to use $ W = \frac {\epsilon_0}{2} \int E^2 d\tau $ didn't work as the integral goes to infinity at r=0. So I used $ W =\frac 12 \int \sigma V ds$ where $\sigma$ is the induced charge on the two surface at radii a and b.

$$ W= \frac {q}{8\pi \epsilon_0b} (\int _{r=a} \sigma_a da - \int_{r=b} \sigma_b da ) $$
which come out to be zero as each integral is equal to $q$. I think this is wrong. How do I solve this problem?