What database are the tables in? What data type is the date column?
I can think of a way to do this with a column of the dates casted to varchar/text, then reference that column as the source of the dropdown values. You might have to make a Model or a database view to create the text-ified column. You need to use a native query for the main query, though, so you can cast the text filter value back to a date type, otherwise you’ll get a type mismatch when the query runs (depending on the DB). This also assumes the string format is easily interchangeable with the date type in your particular DB.
A date makes this a bit easier since they are not timestamp aware and the formats are generally well defined. “Generally” I say, it shouldn’t be a problem if you are taking what the DB sends out and feeding it back to it. Don’t try to localize the format (i.e., change it from m/d/y to d/m/y) or you will have to undo it later and it will be messy.