The little screw does not hold the wedge in.
In fact, it is designed to hold the wedge out.
The barrel wedges are tapered and the further you drive them in, the more the barrel moves back towards the cylinder and the frame.
Ideally, the barrel will seat against the frame at the bottom at the same time that the very end of the wedge sticks out of the right side of the barrel about 1/16 of an inch. Just enough to allow the little finger on the spring to catch on the barrels surface.
With the wedge in this position, the little screw should be backed out until it stops against the head of the wedge. That way, every time the guns wedge is pulled to clean it or to change cylinders, when the wedge is driven back in it will hit the screw head and stop at the correct position.
When I said Ideally, it was because this is not a perfect world and the Colt design is not a perfect design.
The tolerances of all of the parts results in the tip of the wedge sometimes ending up just flush with the right side of the barrel and on other guns it may stick thru quite a ways.
Rather than worrying about the end of the wedge, the thing to look for is that the barrel is tight against the lower frame.
Yes, some of the companies ship their guns with the wedge installed VERY TIGHTLY. It will come free if you use a brass or bronze rod as a driver and hit it with a hammer soundly.
I think the companies don't lubricate the wedge properly when they install it at the factory.
It should always have a light coating of grease on it and in the slot thru the cylinder pin.
While I'm talking about removing that wedge, be careful not to get your finger in a place where it will get whacked if the wedge suddenly moves totally out of the slot. I say this from experience.
Pistols nipple wrenches are a bit smaller in diameter than the typical rifle wrench to allow them to fit down into the recess around the nipple.
There are several companies making them but this is not the place to save a few cents.
The better ones are heat treated so they will last while the cheap ones are often left soft.
If they are soft the little fingers on the end that grab the flats on the nipple will get marred up or will spring open and not return to their original shape. Worse, some of the cheap ones will break if forced too hard.
Once the nipples are removed I strongly suggest that you apply a thread "anti-seize material that you can get at an auto supply store.
These threads seem to have a real liking for getting stuck because of the fouling from shooting.