Here is little easy hack I just made that you could use.

Code:
Private Function RemoveFocus(ChkBox As CheckBox)
Static FakeButton As CommandButton
    
    If FakeButton Is Nothing Then
        Set FakeButton = Controls.Add("VB.CommandButton", "FakeButton")
        With FakeButton
            .Move -300, -300, 30, 30
            .Visible = True
        End With
    End If
    
    With ChkBox
        If .Value = vbChecked Then .Value = vbUnchecked Else .Value = vbChecked
    End With
           
    FakeButton.SetFocus
End Function
To use it all you need to do is call the function on the checkbox_mousedown, better if you use array.

Example 1 (Array)
Code:
Private Sub Check1_MouseDown(Index As Integer, Button As Integer, Shift As Integer, X As Single, Y As Single)
    RemoveFocus Check1(Index)
End Sub

Example 2 (regular, non-array)
Code:
Private Sub Check2_MouseDown(Button As Integer, Shift As Integer, X As Single, Y As Single)
    RemoveFocus Check2
End Sub
Note: Do not add to the CheckBox_Click event because it will cause 'Out of stack space' error.