Those wires pass below the horizontal mounting plate inside the chain locker, then through a hole in the aft bulkhead of the chain locker and into a narrow space between the aft bulkhead of the chain locker and the two lightweight removable panels at the forward end of the Vee berth in the forward cabin. Your boat is the same size and age of my B36, so it’s unlikely that the setup will be any different from mine.
Within that narrow space, you will be able to join in to the original cables that run from the solenoid Located behind the switch panels at the chart desk.to that space, and most likely you can join the new windlass cables directly to the original supply cables.
The panels across the forward end of the Vee berth are held in place with cross head screws, each fitted with a creamy white coloured plastic cover over the tops of the screws. These covers sometimes tend to ping off and might be lost so take care not to lose them as there is a deep void space that is difficult to access, but which you can see into from the forward cabin. On my boat ithat space contained a quantity of water which I was able to extract using my engine oil vacuum pump to remove it.
Once the screws are out you will be able to remove those two lightweight panels, one at a time. They are a bit of a struggle, and even more so when putting them back after the job is done, but they will go back into place. Take care not to damage the soft plastic covered lining material on the face of those panels.
The hole through the aft bulkhead of the chain locker for routing the power cables is sealed using a good quality sealant (Sika) which in the first place you will have to cut it away to get the old cables out, and after putting your new cables through it you will then need to reseal the hole which tends to be out of sight when looking from the chain locker, but relatively easy to get at from the forward cabin. Some medical rubber gloves are handy here to massage the sealant into place.
Regarding connecting the wires together, if I remember correctly the wires are fitted with an eye or ring connected crimped on at the ends which are joined by using a bolt. There is no connector box as such, and in fact on my boat I found those wire connections were not even insulated and were hanging loose where it might have been possible for the wires to touch and short circuit with consequent risk of fire. Having found that situation I covered the connections with self amalgamating rubber tape. This stuff is slightly sticky, but as the name suggests once it is bound tightly to the cables and to itself the rubber fuses together with each layer.
If you have to travel taking your new windlass with you, it could be worthwhile to have the fittings for the ends of the new cables crimped on in readiness for when you get there if they are not already fitted. Obviously the size of the crimped fittings are important, and I do not recall what size wires were used as I didn’t have to replace the main cables. I did have to replace the signal cables used for the up/down hand controller I had at the time. Those signal cables (two + and one -) only carry a very small current to enable the solenoid switch to operate and from that solenoid back to the windlass, the main cables for the current are sized like those used for an engine starting motor. The signal cables for the up/down directions do not actually connect to my Lofrans windlass Which I am assuming you have, though if you have a different windlass your situation may be different from mine.
I hope the job goes well for you.