Those weapons are usually called T1 Summon weapons since they are from the easiest non-omega raids. There are no way to convert their normal version in the ancient/olden version. The ancient/olden version is far rarer to drop and pricer to purchase, the normal version are almost never used in any grid since Primal grids have far better weapons.By the way, what's the deal with primal weapons? why are there two versions of them? I've gotten two cortanas but have no Hades to boost their skills, are they worth using in a Celeste grid or is there a way to change them to olden cortanas?
If you are in HL just purchase a single Olden Cortana in the pendant shop and forget about it.