Yes, you read that right, or well... maybe you didn't. Either way I'll elaborate.
Okay so imagine spells, cast in your sword-hand, not the off-hand, where the spell transfers to the current equipped weapon.
Example 1, a simple fire spell: ignites the blade, or arrow, or bolt, etc. This would do some sort of burn damage, or maybe something like "Scorch" damage where it doesn't last like a burn does, just staggers the victim and does a little extra damage. Oh yeah and the weapon ought to be tastefully on-fire (like Beric's sword from Game of Thrones).
Ex 2, frost: lays a blue frosty ice over-lay across the sword, and you are essentially freezer burning everyone with this like the "ice-cube challenge of 2010's.
Since the concept isn't to make the sword ridiculously OP, just utilize an aspect of your magic abilities, it shouldn't negate the ability to cast other spells with your off-hand, whether reserving that for a ward, heals, or extra dps.
I have literally ZERO notion of how to create anything like a mod, so if anyone were to make this, steal my idea, take it as your own. I want no credit, just message me in secret to tell me it is available to play, that is my price.