I don't think you'd be able to set up the skimmer externally without a sump, because you would need some way to pump the water back up to the tank once it exits the skimmer.
I've never heard of anyone using the filters that attach to the tap, but they don't have very long life spans so replacing the cartridges would get expensive. Plus, they do not use reverse osmosis or deionization to purify the water (RODI), as far as I know, most are just carbon filters, so I don't think it would do the job for a fish tank.