If you are washing and squeegee-ing, on oxidised frames the only problem you should have is the odd line on the glass where perhaps you were not as accurate with your squeegee passes as you should have been, and perhaps teeth gritting frustration with detailing

If the frames are oxidised it is a good idea to pre-detail priior to squeegee-ing the glass, this way you should eliminate the need to dry-detail the glass, and thereby avoid your scrim or microfibre cloth getting in contact with the frame.
But keep the cloth you use for any pre-detailing separate from any that you use for normal detailing, you wantto try and avoid getting your clean cloth's free of contanimation from the oxidised frames as much as possible.
If you go back onto a window to buff it clean, and the glass is dry, then you are almost certainly going to leave marks and smears behind that will be visible from the inside.
If your detergent solution is too strong you will have problems, doesn't matter whether you are using washing up liquid or specialised liquids.
The more detergent you put in, the bigger the film you leave behind.
That glass you have just made a squeegee pass over may look perfect, and to all intents and purposes it is, but there is still a microscopic film left behind.
Don't believe me?
clean an inside window, get it so perfect that niether you nor I could fault it.
If that pane isn't cleaned for a few weeks then as a film of dust/weathering/smoke and so on slowly settles on it, those microscopic particles will highlight every pass you made, and every turn you made of the squeegee.
It only does this becuase of that iinvisible film you left behind that is 'sticky' to these particles.
Pub windows are an absolute sod for showing this up, even after just a few days
you may have wonderful 'glide' when you have a lovely slippery solution in your bucket, but you are far better off developing your squeegee technique instead, you'll find that the specialist detergents work fine then...and as their dilution rates are so much lower than you would use with the likes of fairy liquid, thte residue they leave behind is infinitely less than that left behind by water with washing up liquid in.
And that will also have a bearing on oxidised frames....
Ian