This problem should be solved by a simple analysis.
Assume the force needed to compress the spring is appllied by a circlip plier between the two hooks. This force F has a vertical component V=~0.93F and an horizontal component H=~0.36F (estimated from geometry).
Now assume also, for simplicity, that F acts onto the outer hook, while the inner hook is connected to a pin.
The bending moment in the spring due to V is -Vr sin(theta) (theta from 0 to 1.5pi), and the moment due to H is Hr(1-cos(theta))
So the average bending moment in the spring is Mave=Fr*integral(0.36*(1-cos(theta))-0.93*sin(theta))/1.5pi=~-0.24Fr
From the relationship (delta r)/r2=-Mave/EI, with delta r=0.2 mm, one obtains F=46 N
This seems a relatively high value, so please correct me if I'm mistaken