What is inside an oil filler/breather cap?

You could try using methanol (methyl alcohol) it will loosen debris, remove varnish build up, not destroy the filter media, and it will dry without needing a water rinse.
Alternatively you could use isopropyl alcohol (rubbing alcohol is too dilute) but it takes a bigger amount to do the same job as methanol.

You could shorten they drying time by using gentle compressed air.
I wound up using denatured alcohol. It really wasn’t very dirty. The only thing that came out were orange paint chips I guess from the oil cap scratching the valve cover paint. I poured some engine oil inside but didn’t get the feeling there was any kind of filtering material in there.