It's easy to use the transmute spell to turn iron ore into silver ore.
While true, the spell will automatically convert the silver ore into gold on the second cast, and you need 2 ore to make 1 ingot. You can still craft jewelry that way (and this is how I'm leveling smithing on my Khajiit) but not the same material as the op wanted.
Why the developers didn't find a way to make Silver->Gold on double cast instead of single I'll never know. Would've made the spell much more versatile.
EDIT: In case it wasn't clear, I was contesting the ease of use with regards to iron->silver transmutations, not the possibility. When forced to constantly drop the silver ore and recast, the process becomes tedious.