Mustache softening help [UK]

Hello!

I am trying to grow out my mustache into a handlebar or similar, however I am finding life with a mustache irritating most of the time, wuite literally. My upper lip gets agitated by the initial overgrowth of hair that covers it.

I could use soaps and similar designed to soften the hair, but I have extremely reactive and dry skin (bad issue with eczema).

Does anyone have any suggestions on how best to treat the mustache so that it feels softer, or at least less prickly on my top lip.