From what I know about G body wiring, the 403 will require less wiring than the 307 since you are not using the computer. The sum total of the items to be wired are the A/C compressor ( 2 plugs, only go on 1 way), Distributor ( 1 wire), and starter solenoid ( several wires, but they are obvious). The only one that may confuse you is the starter solenoid activation wire as there are 2 terminals it can be installed on. One is for the old resistance circuit for a points ignition and is not used, the other is from the ignition switch which is used. Put the nut back on that post when you remove the engine and you will know which one it is when you put it back on later. I think they are marked S and R, so there is a reference if you don't do that. All the other wires on the solenoid go to the BAT terminal post, which is the big post that does not have a wire or strap running down from it to the starter. This is the main terminal bus for the whole car, so the battery positive cable and 3 or 4 fusible link wires are all put on that post with large gauge ring terminals. You will have 1 wire for the oil pressure idiot and another for the coolant temp idiot light too. There is also 1 for the choke heater (if your carb does not have an electric choke, swap the cover from the 307's choke. It's a perfect fit and electric chokes are nicer than heated ones). One last thing. The alternator is simple. It is 1 post on the back for the big red wire, and 1 connector (white with 1 orange and one red wire) that can go nowhere else. Now if you have the gauge package, this adds another 3 wires. One is for the tach and it is a white wire that goes on the distributor terminal marked "tach". Another goes to the oil pressure sender, and yet another to the temp sender. Almost all of them will be obvious if you put the harness on the engine like it was on the 307. I use "range of motion" when trying to find a connector I missed and don't know where it is. To do so, just take the wire and scribe an arc with it from where it comes out of the harness. The right place to put it is within that circle. 99% of the times you will not find anywhere else that a wire can go within that circle, and if you can, just look for where it would naturally fall and remember that it should not be taught when connected. I have replaced several wiring harnesses and rarely have a problem. If all this is confusing, don't let it be. All you really need to make it run are the starter, alternator, and distributor. Those are things you should already have done at least once on some car, and doing them with an engine change is no different.
ADVANCED SWAPPING TIPS: Wire the engine out of the car. This is not mandatory, but it is how I did it when I put the Chevy 355 in place of the Buick V6. I put the engine and trans together, along with the manifolds, alternator, power steering pump, brackets, etc. before I put it in ( I did my car with the front clip off). I then took a second wiring harness (from a Chevy powered 85 G body) and put all the wiring in place before I put the engine in. I even installed the + battery cable and it's brackets. That way, All I needed to do was wire up the battery and plug the bulkhead connector in to the firewall when it was in. If you want to do this, the bulkhead connector is located below the wiper motor and is held in place by a 1/4 in bolt in the middle. It comes apart into two sections once you remove it: engine and lights. Leave the lights part on the car, but remove the engine part with the old engine (Don't forget to take the bolt out for the chassis ground that is in the middle of the firewall!). Then take pics of how it attaches before you remove it from the engine. Next, transfer it over to the new engine. Now all you have to do is install the engine, hook up the battery and plug in one connector. Just remember that there are 4 subharnesses in the engine bay: Engine main, Computer, A/C and lights. The A/C harness plugs into the main one with a 4 prong plug on the passenger's side(needed to run the heater and defrost), the computer one is not needed for you, and the lights you plug in with the engine bulkhead connector. Also, there are a few grounds that go under one of the upper transmission bolts and it is easier to do these when the engine is out rather than in.
Oh, and if you do do it my way, it is MUCH easier to put the transmission cooler lines in with it out of the car than in. They usually have some clips that keep them attached to the pan rail as they come forward. These will keep them out of harm's way when the engine is put in (unless they hit the core support, but I have never put the engine in with the front clip on). I pull the trans and engine together, and install them with as much hard to reach stuff attached as possible. Remember that those little factory clips and such are there for a reason, and will prevent problems later if you use as much original GM stuff as possible. I even use the factory plug wire looms on my car. Oh, and you can also put all the hoses on the engine before it goes in too. This is really nice when you are dealing with the lower water pump hose as it is sometimes a PITA to get to in the car.
When I did my swap, I had the whole front clip, engine, trans, exhaust, wiring, etc. pulled in about an hour and a half. The engine was still warm when it came out because I delivered pizza with it that night, and had the engine out by 3am. The new engine in my car was a bit more of a problem because of some unforeseen problems that made me order parts (frame bushings, Chevy fuel line, and waiting for the machine shop to rebuild the control arms). You should have no such issues since you are doing a like for like swap. In fact, I put my old V6 in a friend's car and had it running in about a day, maybe a day and a half.