[Wellington]

Sometimes (and I'm not familiar with this set) you don't have to unsolder the speaker connections, you can unscrew the nuts on the four brackets around the rim of the speaker, and bring the speaker out with the chassis.

In your first photo, it looks as if the wires to the speaker have been looped and secured in a simple knot. You could try undoing this and that may give you the length of wire required to remove the chassis and leave the speaker in the cabinet. This depends on the insulation on the wires being flexible, though.