Can it be done? Yes, and pretty much exactly as you describe. The wire is probably 14 or 16 ga. Any smaller than that would be bad.
But, there's no ground wire, just black for hot and white for common. That concerns me a bit.
If I was in your shoes, I'd do a bit more troubleshooting on the 12vdc first. If that wire is cut or shorted somewhere between the slide and the fuse, it will cause problems down the line for sure.
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'11 Cougar 326MKS loaded with mods
'12 Ford F250 SuperCab 6.7 PowerStroke Diesel
Amateur Radio: KD2IAT (146.520) GMRS: WQPG808 (462.675 TPL 141.3)
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