If the question is, do the Swiss as a nation vote with swords, then the answer is “no.”
If the question is, do some of the Swiss vote with swords, then the answer is “kind of, but not exactly.”
There is a canton in Switzerland, Appenzell Innerrhoden, which to this day holds municipal votes via a gathering in a public square, an event known as a Landsgemeinde. In Appenzell Innerrhoden (and in other Swiss cantons in the distant past, I presume), voters have traditionally carried rapiers as proof of their voting status:
“Swiss citizens who are residents of the canton from the age of 18 upwards (until 1992 from 20 years onwards) are admitted. Since 1991, voters with the official voting card are allowed into the square. The men however can decide themselves whether or not they wish to leave their voting card at home and carry a rapier in its place. Until 1991, this rapier was the only proof of being allowed to vote. The rapiers are usually handed down from one family generation to the other and are not normally left at home on this day.”
from: http://www.kantone-web.ch/kantone/ai/en/politik/sitzung/ [bolding mine]
Appenzell Innerrhoden was, in fact, the last canton in Switzerland to approve of the right of women to vote in municipal elections–this was only granted in 1990! However, women had already won the right to vote in federal elections back in 1971–not 1979, as the poster claimed. This was won through majority vote–even though Appenzell Innerrhoden as a canton probably voted against it, they couldn’t block its passage in a veto-like fashion.
It sounds like the poster on that message board heard something about the voters carrying swords at the Landsgemeinde in Appenzell Innerrhoden, and knew that canton was the last one to approve of women’s right to vote, but didn’t get all of his facts straight. The voters don’t appear to actually raise their swords to vote–they just carry them as traditional proof that they are eligible to vote.