What kind of origin could these swords possibly have?

[Aureoled]

Well, if we are going with greek mythology, i think if we use cyclops, who lost their families due to apollo, or something and decided to make these kind of weapon because they hate humans or something because they are loved by apollo or something would make more sense

 

[K5Rakitan]

Let's say someone melted down the iron penis and forged it into a sword because the village was running out of metal in the middle of a war:

Kanamara Matsuri - Wikipedia

en.wikipedia.org

 

[Cipiteca396]

Ug greek gods overdone egyptian slavic or celtic would make this interesting so many european mythos you can use just think witcher.

Yeah, this wasn't very well thought out. If you don't want gods, don't include gods. But even if they have slightly different names, a god is always going to have overlap with other gods. It's in their nature.
The Greeks are the goto example because they and the Romans tended to go to another nation, see a god they didn't recognize, and either decide it was an appellation of a god they did know, or that they should start worshiping this unknown god just in case they existed. The Egyptian pantheon in particular was completely adopted by the Romans, so a lot of their gods are synonymous with Greek gods... Hermanubis for example.