If it is a Georgian mansion then most of the window panes are likely to be of a size that will suit a squeegee very well...however, if there are windows with panes the same size as the kind you will see on normal houses with Georgian windows fitted then you will be way, way quicker to either use a damp microfibre or scrim in one hand to clean the glass, and a dry one in the other to buff the glass dry.
Or again, use whatever kind of cloth that you have (a clean dry one) and mist the glass with a propietary glass cleaning spray (any of the major supermarkets own window cleaning spray is ideal...don't waste your money on the likes of Mr Muscle) and then buff clean with your dry microfibre or scrim.
I have done a great many time and motion studies on the comparisons between a squeegee method and either one of the methods I've described above and using a squeegee, especially on external glass is much slower (small georgian panes) and less effective. ESPECIALLY if you are fairly new to window cleaning, with the sqeegee method you will have no end of kicks and runs to pick up with a dry cloth.
But genuine traditional Georgian window panes (such as you would usually find on a mansion( but not always!
)) are very well suited to using a squeegee.
Ian