That wouldn't work, either.
You can modify the options of the datepicker, and you can use these to limit the range of dates that can be selected from, for example (hidden link), but you can't specify individual dates that can be chosen from.
You could produce a custom solution using Views that achieved this, but it will require some PHP and JavaScript programming.
If you are able to do that, great, otherwise you'll need to find a developer to do that for you (such as can be found at toolset.com/contractors).
The first part is to modify how the filter control is inserted, so that instead of a datepicker you have a select dropdown.
Edit the Search and Pagination of your View. It will have a shortcode wpv-control-postmeta which inserts the datepicker. You can change this to a text input, but not a select, which is what you will need.
So edit that shortcode so that it is a more generic wpv-control shortcode that allows you to create your own filter controls, so that it looks something like this:
[wpv-control field="wpcf-my-date-field" type="select" url_param="wpv-wpcf-my-date-field" values="," display_values=","]
Note that your field attribute will be different (depending on the name of your date field), as well as the url_param attribute.
We specify a select field, and then we provide some options using the values and display_values attributes. I entered a comma for those just so that the select field would be rendered with one empty value corresponding to nothing selected. You will need to provide the actual values with a combination of PHP and JS.
The PHP will be required to query the posts and get the date field values for each post. You will then want to construct an array of these values.
You can then pass this array to the front-end for use by some custom JavaScript using the function wp_localize_script (https://developer.wordpress.org/reference/functions/wp_localize_script/, see here for a tutorial: hidden link).
Your JavaScript can then take this array and use it to build the options for the select input, where the value is the timestamp and which displays a human readable version of the date.
You would add that with the DOM ready event, but you would also need to re-build the select dropdown every time the filters or search is updated, for which you can use custom JavaScript front-end events that you can find placeholder code for using the Frontend events button in the custom JS editor of the Search and Pagination section of the View.
So, if you are familiar with PHP and JS you should be able to see how this is possible, but it is very much a custom solution.
