Wolfish: I disagree with your point because Achashverush actually executed the advisors who recommended he execute Vashti. So, clearly, he publicly made very clear he regretted his decision very much.
The fact that he executed those advisors also indicates Vashti was executed. How she was executed I don’t know, but perhaps Rashi or the same Medrashim that tell us she was killed also tell us how.