Recover Solder (Sn-Pb) from wires
Unfortunately the reason solder works is that it partially dissolves copper as shown in Figure 1 to form $\ce{Cu3Sn}$ and $\ce{Cu6Sn5}$ phases (also known as bronze) shown in Figure 2. Because of this you cannot simply melt solder off the solder wick to recover it as the tin will continue to dissolve the copper forming bronze. There is also the issue of needing rosin in your recovered solder to be useable. This 1960's video from NASA is an excellent video for learning more about the soldering process.


Figure 1. Reactions of the Copper-Solder Interface


Figure 2. Copper-Tin Binary Phase Diagram

To address the acid method. Physically, it could work (I would not recomend doing so with leaded solder) as most ROHS compliant electronics are $95\%+$ tin solders with either silver or antimony added as alloying agents to prevent tin whiskers from forming. That said it economically dissolving in acid then precipitating then reducing tin in a way which does not also produce copper would be a tedious and time consuming process. You are far better off just buying solder which does not cost that much and has rosin needed to flux the solder.