Thomas and Betts is good for connectors, tools, and tywraps.
As far as soldering weakening the copper wire, it is already annealed, so I don't know how that can happen. I have seen reference to strain relief sheathing being used as the solder joint acts as a "stop point" for flexibility in the wire, so the movement stops at the end of the solder joint, and that's where the wire will fail. think of putting a coat hanger in a vice and working it back and forth. It breaks at the vice jaw, as the immobility of the wire in the jaws forces the energy of the movement to be concentrated into bending the wire at essentially a fulcrum point. The strain relief sheath, (this can be done with a couple of pieces of heat shrink) absorbs the bending force into the sheath, so the full bending moment cannot reach the fulcrum point.
I am also one that ditches the sheath and uses heat shrink, unless it is a service joint, in which case a Molex connector from Radio Shack is my preferred part.
Heavier paste flux is indeed corrosive, but there are UL listed non-corrosive flux pastes available. I have used them for years on aircraft.
Also, and very important with older bikes: If the wire looks like anything less than a new penny (sorry, non-North Americans, I don't know if you have copper-clad coins) the wire is already corroding, and should be replaced, as you will not stop it, and crimp or solder, it will eventually fail.
$0.02 in the bucket, I'm done.