Those Properties are stock standard with any Sharepoint webpart as you know.
I have not tested the following code, but i'm pretty confident that this should work:
public override Microsoft.SharePoint.WebPartPages.ToolPart[] GetToolParts()
{
Microsoft.SharePoint.WebPartPages.ToolPart[] myCustomToolparts = CreateMyCustomToolParts();
//Removing the Base Method for calling creating the ToolParts should hide all the Built in Toolparts
//return base.GetToolParts();
return myCustomToolparts;
}
If this does not work I'd suggest some Javascript/Jquery:
function hideToolParts(){
$('#ctl00_MSOTlPn_EditorZone_Edit1g_55d19aab_008a_4d9a_9ca6_db3ad2137f20_LayoutCategory_IMAGEANCHOR').parent().hide();
$('#ctl00_MSOTlPn_EditorZone_Edit1g_55d19aab_008a_4d9a_9ca6_db3ad2137f20_AppearanceCategory_IMAGEANCHOR').parent().hide();
}
Hope this helps.