Will my wires have current stability issues?
There are two problems from the flux (see Why do we need to remove flux from circuit boards?)


Electical conductivity -- this does not apply in your case. A couple of megaohms, or even a couple of kiloohms, will not affect PC PSU in any visible way.
Flux reactivity -- this may apply in your case, but it is unlikely. Again, the PC wires are usually very thick, so it will be many years before corrosion becomes a problem. 


What you should be worried, however, is that if the connectors that were designed for crimping were soldered, the wires can break off much easier. A proper crimp holds the wire by insulation, and soldering most likely has destroyed this. Make sure not to bend wires too much once you have installed them.