Chinese sabre blade believed of late Ming dynasty with svastika markings

[Kubur]

I visited many Roman temples with swastika.

A bit older than Buddhism, Jainism has swastika for symbol.
I don't know if the Greeks or Romans brought it back in their "suitcases"...

As mentioned by David, Swastika is a very old symbol and a very simple geometric design, related to wheel, sun, life... and used by many cultures.
From America to Japan...
So I won't venture in explanations or influences...