Can wudhu be done on the roof with a bottle of water if western toilets hinder foot washing?

We pray namaz at the roof top of the office building. My question is regarding performing wudhu. There are only western style toilets. The main concern is regarding washing of feet, what we do is we perform wudhu in the wash basin dry the hand and face with handkerchief and then take a bottle of water and wash the feet on the roof. Is it allowed? Washing the feet is not possible in the bathroom as the floor is very dirty also the socks and shoes get wet. We can’t use much water there to perform full wudhu as the admin may object as there would be water logging. Please give a detailed answer to it.