As I understand it, you CAN NOT skim it out once it's in. At all. All you can do is dilute it to the point of usability.
Zinc fully alloys with lead, so it will never separate out without a caustic chemical reaction. What does separate and float at the surface is tin, which will not truly alloy with lead. It forms an amalgam, which routinely separates out, but can be fluxed back in. This means if you are skimming the shiny top off, you are probably tossing your valuable tin.
With the Zinc melting at 787F, and the lead melting at 621F, it is possible, and relatively easy to melt the lead and scrape all the other junk off the top. But it has to be a slow melt since the base of the crucible or pot will be hotter than 621 to melt the lead, and in a fast melt it may be significantly higher. I use a wick type kerosene stove to temper my patience since it is so slow as to be almost impossible to overheat the initial WW smelt.
Also, Zinc will contaminate the melt *before* melting point but at a *very* low rate. Similar to tin mixing (449F) into lead. Tin will mix into lead at temperatures WELL below it's melting point. A technically inaccurate but very good illustrative description is melting away a lollipop in your mouth. (ERROR! Note below)