On the chance that Hatteras may have made changes to the 44 TC over time, let me qualify my remarks as applying to 1968 and earlier 44 TC production. From being on other, later boats, I believe they all had the same electrical components, but I have not done a detailed inspection on any boat other than the one I owned. Once you read my description it will be easy enough for anyone interested to verify if the same conditions exist on any individual 44 Tri Cabin. BTW, I owned mine between 1982 and 1985.
With that lead in, let me say that there was not any aspect of the electrical system that was impressive, both AC and DC. Let me start with the AC system. The standard double 120 volt outlets were not mounted in boxes, exposing many of the electrical connections to the salt spray coming in the engine vent area behind the paneling. The wire used was not tinned copper, just bare copper and coarse stranding. Looked like auto wire. When you tried to renew a connection, no matter how far you stripped the wire insulation back, the copper was black since the insulation was not up to salt air intrusion. The breakers in the distribution panels were house hold single poll Square D thermal breakers. The shore power inlet rear connections were open with no protect on the rear for safety or corrosion protection. The DC system carried many of the same components. Non tinned wire subject to salt air intrusion in the engine room and bilges, AC rated Square D single poll breakers used for 12 volt DC service, and my all time favorite fire waiting to happen. On the DC distribution panel was a selector switch for the source of 12 volt house power. It had four positions. Off-Port(1)-Starboard(2)-Both. The battery wires servicing the switch were #6 coming off the two battery banks with no fuse protection. Each battery bank was two paralleled 8D's. So one day you decide to use the "BOTH" position on the switch to get max DC power at anchor. When you do this you tie the two battery banks together using two 15 foot lengths of #6 wire. Then one engine decides that it does not feel like starting and cranks for 10 or 15 seconds, two or three times. The result is you melt the insulation off the two #6 wires and also melt and short the adjacent wires in the wiring harness up to the distribution panel. How do I know? The hard way, I did it, and did all the rewiring to fix it. If you have a boat with a selector switch as I have described, NEVER, NEVER, have it in the "BOTH" position when starting your engines. Enough said?
BTW, starting in the early 70's as new models were introduced the electrical systems vastly improved to the best in the industry, in my opinion. Our 1976 LRC has electrical systems equal to or better than anything you see in today's current production. I also owned a 1975 36 Convertible that had a very good electrical system. You just need to understand what you have and treat it accordingly.
Pete