Camera Connection issues

I decided to overhaul my 3 camera analogue system, replacing 2 cameras with full HD SDI cameras and a new hybrid DVR to accommodate the 3rd analogue camera. Replaced one old camera with new dome no problems at all and surprised to see that the new camera works with the old DVR. Problem with 2nd camera connection though. Its a high spec 12/24 volt camera which comes with not a bullet power connector but a screw in type connection requiring the power feed to be split in to 2. Sorry if this is a bit complex but can I cut off the dc supply bullet connection. Stip back the wires (centre positive, outside sheeth negative ) then feed them in to connection and end up with a picture. Naturally there is a 2nd bnc connector for the video feed.

New Hybrid dvr hitched up , 2 cameras (1 analogue + 1 HD SDI ) but still problem exists with the camera as shown in picture. Been told by supplier that rg58 cable is sufficient but wondering if I will have to rewire this camera with something else. Is there something I am missing out of the equation ?

should be ok- I have done this with Panasonic dome cameras which have similar connections.

Yes, cut off the butt connector, split the wires, and plug them it, it's all the same just different ways to attach power to the camera.