oh smart, it probably wouldnt stick to the metal threads and the screw could be cooled water
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Yeah, it should work. Its relatively easy to get solder to stick to copper.
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The silver color of solder will stick out like a sore thumb though against the warm copper color.
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Solder paste can be applied evenly and in minimal amounts. YuvalS double wrap strategy should hide it well. Without the double wrap I still think it could look good, the uniformity of the solder application mattering the most, aesthetically.
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Last year I have tried soldering. The problem is thar the screw is a huge heatsink and absorbing all the heat so I am not able to solder the wire while it is wrapped on the screw.
I am also can not add glue on the inside since:
- I first ha e to remove it from the screw
- The scew need to fit inside the wire wrapping to enable battery replacement.
For the 2nd try I have added lubrication. First I had to remove all the Epoxy from the wires, then I renewed the Teflon tape and sprayed it with WD40.
I have also changed the glue for a bit more flexible gorilla glue so it will not break so easily while unscrewing.
I will not let you wait and tell you that it broke apart just like on the previous tries 
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to solder it could you not use a stove/blowtorch to get the screw and copper super hot and melt the solder on instead of a iron
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I feel your pain YuvalS! 
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This is after the stove
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