I’m afraid I have to disappoint you. The story of the two meanings of the novel’s title is an urban legend. In the old Russian orthography the word ‘mir’ had two spellings: миръ, meaning peace, and мiръ, the society, the universe or the rural community. Now, few people remember which word meant what.

So, the editions of War and Peace published before the orthography reform of 1918 show that the original title was Война и миръ (see, e.g., the title page at the Russian Wikipedia article about War and Peace.)

In a 1913 (or 1915, I’m not sure) edition there was a typo, where on one of the first pages the title was written as Война и Мiръ. Probably, this was the source of the legend. Also, in 1916 Mayakovsky wrote a poem named Война и мiръ. This pun only increased the confusion which started spreading after the old orthography was forgotten.

There’s a web page (in Russian) about this story.

BTW, in an old school joke it is said that the boys read war and skip peace, while the girls read peace and skip war