I think 95% is a high figure. The true figure is probably closer to 70% -80%, and that's only counting "adult men."

That however is still a shocking number. It stems from the insane degree of militarization that Paraguay had during the period. They only had a total population of 500,000^§ or so. The allies (Argentina, Brazil, Uruguay) had around 11 million. And yet the Paraguayans fought multiple times at near parity. At the First Battle of Tuyutí Paraguay fielded 25,000 men vs the allies 35,000. In that one battle alone, Paraguay lost 5-10% of its adult male population. And they had several battles like that, with the war extending five and a half years. Their total field strength was kept around 60,000 for most of the war. Francisco López held increasingly severe conscriptions until age ceased to be a meaningful distinction. Virtually every man in the country was conscripted.

By the time the Duque de Caxias and other leadership reached Asunción the war had turned brutal and Asunción was sacked in the old meaning, and that was hardly the first town put to the sword.

There was a census in 1871. That showed the total population had been reduced by roughly 2/3 and out of 221,000 inhabitants, less than 29,000 of which were adult males.

§ It should be pointed out that prewar population estimates of Paraguay are all over the place. I've picked a midrange figure. People have tossed out higher numbers, up to 1.5 million. Which makes that 1871 census look far worse. But consensus seems to agree that a population of 400,000 to 500,000 is most likely.