There are no hooks into the data export

But you can create a custom export type that has a setting (datepicker) so that the user can select a date and then use the selected date...

So default cv export looks like

public class ExportToExcel : ExportType {

    public ExportToExcel() {
        this.Description = "Exports all data to a csv file";
        this.Name = "CSV File";
        this.Id = new Guid("94ED105A-87B3-4e1f-97CB-9A320AEE2745");
        this.FileExtension = "csv";
    }

    private string xslt = Configuration.Path + "/xslt/excel.xslt";

    public override string ExportForm(Form form)
    {
        RecordsViewer rv = new RecordsViewer();
        XmlDocument xs = new XmlDocument();
        XmlNode XmlRecords = rv.GetXmlRecords(form, xs);
        rv.Dispose();

        return XsltConvert(XmlRecords, HttpContext.Current.Server.MapPath(xslt));
    }
}