You have this backwards. Samurai swords were thicker to begin with. .
OH?
"It was the attempted Mongol invasions of 1274 and 1281 that the japanese nation faced its greatest military crisis. In the first action it was saved by a great storm which sank the intire Mongol fleet.
In preparation for a second invasion the Bakufu sent edicts to every province ordering great efforts to be made to imporve naval defenses and military capability.
One of the results of these efforts a magnificent new style of sword with it's great width and thickness at the ridgeline."
(The Japanese Sword, page 54)
What we see then is that before the Mongol wars the swords of the Japanese were not really aimed at fighting someone who was wearing much of any armor.
(On page 29 of this book you see what was a design of the very early swords in Japan...a long but knida thin blade. )
Another basic change to the design of the Japanese sword is that we see the introduction of a ridge line in later swords, whereas the early swords lacked a ridge and were flat sided.
When the Mongols came to Japan they made use of very heavy armor and liked to use horses, and thus the weapons the Japanese started to make at that time also reflected the basic change in the way wars were being faught.
The Mongols didnt stop to meet the people they were going to fight, and introduce themselves and talk about their family history as was common amoung the Japanese.