The white/yellow is not pus - it is sloughy tissue at the base of the wound.If you don't have a scapel a sterile syringe needle would work as well to make a puncture in the middle of the "squishy" area. But before doing that, have you put pressure on the squishy area to see if it moves any more puss out of the open area? If not gently do that. Antibiotics are a must. Don't worry about the white under the back scabs, that can heal over time, but if there are any other very large ones that have this sort of puss in them they need to be cleaned.
*sigh* In the US it still seems to be the practice to scrub wounds until they bleed. Here in the UK that approach was discontinued years ago as not being best practice. Unless the wound is full of grit or dirt (as in an RTA) then scrubbing the wound does little to aid in the healing process - all it does is remove any delicate granulation tissue which might be forming & is intensely painful.I just sat here debating if I should recommend this or not, but I will and let you decide if it's right for you. Generally with tramatic wounds that cover a large amount of skin, particularly burns, it is advised to use a gauze pad and clean the affected area 2-3 times per day, rubbing it until it bleeds just a little. This would be acceptable on the back, since I can't see the head wound in person, I don't know for sure. If the yellow I see is in fact puss covering the skull, then it would be difficult. Ideally that wound on the head needs the dead tissue around it cut back and stitched by the vet to promote proper heading. Ooops, that reason for the scrubbing until you see a little blood is that it promotes better healing by increasing the blood supply to the area encouraging it to heal better and fight infection because of the antibodies that the blood brings in with it.
Slough is removed by a process of autolysis - you can mechanically debride wounds but often the slough or fibrinous layer will reappear. All that is really required is a moist environment to assist the body's process of autolysis.
I certainly would not scrub that poor kit's head wound.