Using that logic it would be perfectly fine to use the mythology to add to the world but blatently disregarding the source material brcause you want a silver sword isn't taking from the true mythology. The books were born of the mythology as well, Riordan did a lot of research into a subject that isn't always clear on a lot if points but I do know that there is never a mention of silver having any sort of magical properties. That is common legend but it is not part of greek myth.

If you want a silver weapon that much then say it was mined from the fields of punishment and cooled in one of thd damned rivers or the metal was melted down fro hunters weapons left behind or something but don't go ignoring the natural rules because you want a special sword

Athena tricked Hera into breastfeeding Hercules when he was an infant granting him immortality. There are a handful of variations on the subject but that is the favoured one.

Medusa was decapitated with a sword granted to Perseus by the gods, not a normal blade.

But putting all of that aside there is never any mention of silver having an effect on anything in greek mythos. Oh and the special thing about the maguc metals is there ability to dust greek monsters.