It depends: if the eels are eating well and have good body mass, treating with a chelated copper like copper power or coppersafe can be a good option. What typically happens is that the eels *may* go off feed during the treatment. If they were eating well before the treatment, then they will resume fine after it is concluded (even with the standard 30 day treatment). However, especially with zebra morays (that often arrive not feeding well, and thin) treating them right away with copper just extends that starvation period, and that can be a problem.
Ionic copper like copper sulfate or cupramine is not a good choice. That is the basis for what you will hear, "don't use copper on eels".
It also depends on what parasite you are targeting. If it is marine ich, then hyposalinity could be an alternate therapy. However, that won't work for Amyloodinium (velvet).
Chloroquine might be another option to control protozoan parasites, but it can actually be harsher on fish than copper is. Chloroquine requires a fairly high dose ( 20 ppm) to control active infections, so adverse reactions are more common than is seen if you are using it as a preventative, or to control a minor infection, and are dosing it at 12 ppm.