For this camera you do not need a CPL, a plain polarizer is sufficient.
In general lenses that have a built-in telescopic shade, have it surrounding a filter thread fixed to the barrel. Thus you retract the shade, screw in the filter and extract the shade again. Have a look at the built of your lens.
The only issue this design has is that with any filter in need of turning one must retract and extract the shade any time one wants/neds to adjust that filter. Also some of these turnable filter come with a lever. One must be able to take it off to still be able to use the shade.
If the filterring is built into the shade, that these problems do not exist. Though now a filter may be inadvertedly being twisted by twisting the shade.
I think there were even lenses that yielded fiter threads at both, barrel and shade.