All conductors (as differentiated from superinsulators and superconductors*) are lossy, so it doesn't really matter. You're actually making things worse by choosing a lower conductivity, but kind of maybe not it depends.
What are you doing, what are you trying to do, and how?
If you have waves building up inside the enclosure, it may be worth adding some absorber material, to dampen resonances.
Inside a typical sized boxy metal enclosure, these will be cavity resonances at UHF to microwave frequencies, with especially strong coupling to charged nodes or current loops in certain unlucky locations, depending on frequency (mode).
If you have waves building up inside, and little absorption inside, the waves may end up finding their way out of otherwise seemingly inert gaps, slots, holes, whatever. EMI tape, springs, etc., and mechanical redesign (perhaps including more overlapping seams or fasteners), are good mitigation.
This all seems rather unlikely for what you're probably working with. Hence the question; what are you doing, etc.
Far more likely, your concerns are down to conducted EMI along cables, and the enclosure could be plastic (perhaps metallized plastic) for all that matters.
*Superconductors exhibit zero resistance, thus perfectly reflect incident energy; this is only true at DC, and not quite true at AC. The best superconducting resonators are made from spun niobium, and exhibit a Q factor in the 10^7 range at 800MHz. Superconductivity does not have infinite bandwidth; it must, necessarily, drop off at some point, and that drop will be accompanied by losses. This is typically in the THz to far-IR band, which is why superconductors -- high-temp ceramics in particular, which are always black -- do not suddenly become impossibly shiny when they cross below the critical temperature!
Conversely, superinsulators... aren't really a thing, sort of. There are topological insulators, which are unexpectedly well-insulating, except for surface states if applicable. Plain old vacuum, absent any charge-carrying matter**, is about as good as we can get. After all, we can see light from the furthest reaches of the universe, and that's a pretty long trip. Anyway, if we had lossless insulators of non-vacuum permittivity, we could use alternating layers to make a dielectric mirror (at least for a given frequency range) of arbitrarily high reflection and zero loss, to the same end.
The more fundamental point being, there is symmetry, an equivalence, between zero and infinite conductivity.
**Note that this is still a bit exceptional, as the best vacuums we can produce, still have cosmic ray radiation zipping through them; collisions with walls produce showers of charge carriers, and the particles themselves are often charged (e.g. super high energy protons). These cause conductivity to be strictly nonzero over the long term. Such conductivity might be low enough that we are unable to observe any impact on, say, transmission of low frequency EM waves, over any scale of vacuum vessel we can construct on Earth.***
***And just to get really into it... We have known for quite some time, that interplanetary space is in fact full of radiation. Solar wind is a plasma, true it's tenuous compared to most lab vacuums -- but over astronomical distance scales, it behaves as just any other charged gas does, trapping magnetic fields, carrying momentum, shocking into surrounding (interstellar) gas, etc. (And so on up the scales, to galactic clusters and intergalactic media, which are even lower density still, but nonetheless nonzero.) It's noteworthy that plasma has a cutoff frequency, above which it doesn't block EM radiation; for the Earth's ionosphere, this is ca. 30MHz, which is why shortwave communication can bounce around the planet, but VHF+ flies out into space. For interplanetary media, this cutoff is some kHz, above which we have relatively unimpeded view of the universe, and below which it just looks like you're surrounded by whatever noise the solar wind contains (much like trying to observe sunlight on an overcast day, or view IR radiation inside an oven).
Tim
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