Depends on the headphones, the amplifier, and how you define "degrade". Do you count lower volume as degradation? How about an altered response? Or what else? If something is changed by a miniscule amount you probably would never notice, would you call that degradation?
For the cabling itself, the thickness, shielding, and geometry are much more important considerations than metallurgy, as long as you're using a reasonable conductor like copper (as far as effects that seem to line up with theory and that have actually been confirmed). The metallurgy gets some kind of disproportionate attention in audiophile circles for various reasons.
Usually the effect should be minimal.
So what are the headphones, and what are you plugging them into? Just out of curiosity, what do you want 25+ feet for? Keep in mind it's also possible to use extension cords.