Why would you care what Achasverous would eat? He was a very wicked king...
In my humble opinion Ahasuerus chief character faults were stupidity and apathy, more so than outright wickedness. He was fed bad information about Jews [he was made to think they were a threat, and who does not take threats seriously?], and in the end he did not murder the Jews, instead he put wicked Haman [ys"v] to death [for lying to him about Jews] while Blessed Mordecai the Jew was elevated to the high position which Haman [ys"v] had previously occupied [chief adviser to Ahasuerus]. His son, Cyrus the Great [another historical figure who may have eaten these cucumbers], freed the ancient Israelites and sent our people to build the 2nd Temple. Ahasuerus is also known as Xerxes, to me he is historically interesting, and he was most likely a Zoroastrian in either case and I have studied Zoroastrianism in comparative religion. All of the old Persian kings gave the pagan Greeks [who except for Alexander the Great were terrible to the Israelites] a hard time.
Ezra and Nehemiah, along with the Jews who spent time in Babylonian slavery, might have eaten these cucumbers too.
I suppose "Ach-my-dinner-jacket" may eat them as well, and we can all hope that he chokes to a painful death on one.