Does this code do what you want (note that I removed some of the variables you declared which were not needed for this code, so if you need them later, you will have to Dim them again)...
Code:
Dim ColLetter As String, SavePath As String
Dim VisibleRows As Range, WS As Worksheet, wbOld As Workbook, wbNew As Workbook
ColLetter = "K"
Set wbOld = ThisWorkbook
Set wbNew = Application.Workbooks.Add(xlWorksheet)
Set WS = wbOld.Worksheets(1)
WS.Rows(1).Insert
WS.Cells.AutoFilter field:=WS.Cells(1, ColLetter).Column, Criteria1:="Y"
WS.AutoFilter.Range.SpecialCells(xlVisible).Copy wbNew.Worksheets(1).Range("A1")
WS.AutoFilterMode = False
WS.Rows(1).Delete
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