Well, we've seen a bunch of non Sith bad guys have lightsabers in the past, and even in canon Grevious liked them. I think its a bit presumptive to assume snoke won't have one, and especially to assume that Kylo only uses one because of his grandfather. At a bare minimum, as a group that seems to be in opposition to Luke Skywalker (based on what we know of Kylo betraying Luke and then just being part ofd the dark side in general), it would make sense for Snoke/Kylo to have lightsabers since, while not technically Sith, they'd use lightsabers or similar weapons to fight Jedi.
So, Snoke might not have a lightsaber, although I'd be legitimately shocked if he doesn't because a Snoke/Luke saber fight not happening is pretty unlikely in my opinion. But I definitely bet that Kylo isn't specifically using a lightsaber because of his grandfather.
Ben/Kylo using/having a saber in homage to Anakin/Vader isn't speculation; it's confirmed factual information.
Also, we saw Grievous using captured Jedi sabers purely for the physical power they provided since he was not Force-sensitive, something that has been made even clearer and more obvious with the new lore that has emerged since 2005.
The only significant non-Sith Dark Side Force-wielder we've been introduced to is Mother Talzin, and she did not use a lightsaber, which was our first explicit indicator that the use of a lightsaber is specifically a Jedi/Sith thing.
Both Ventress and Savage Opress used sabers because they had officially been taken on as Sith apprentices.