This code will delete the blank cells (same as you selecting the cell
and deleting to the left). See comment in code below to move cell up
instead

Sub delete_blanks()
For myCol = 1 To Selection.Columns.Count
   For myRow = 1 To Selection.Rows.Count
       If Selection.Cells(myRow, myCol).Value = "" Then
           Selection.Cells(myRow, myCol).Delete Shift:=xlToLeft
'change this to xlUp if you want to move cells up when you delete
       End If
   Next
Next

End Sub