My suggestion is to buy the chassis mount version of the connector that you display, plug in the original SOtM cable and use a continuity checker to find the two terminals that are connected to the hot plug of the dc barrel connector. Mark them with red nail polish (or something). Then you will be set. Insert the cable plug before doing any soldering, and you have a guide.
By the way, when soldering make sure to bare only a tiny bit of the wire before tinning. It is very easy to short that connector. Use good lighting, a strong pair of drugstore magnifying glasses, and you should be ok. I've made half a dozen of these and I've never gotten away without using teflon tape to isolate the two hot wires from the neutrals. Good luck!