welcome to the forum MKL.
when I make Stilton I get upset if there is no mold on the outside, I never try to scrape, brush or wipe the mold off, sometime's I will get some white hairy looking mold, then I will take some vinegar and dab the spot with it and I try to avoid killing off the desirable molds (blues, greens, geo)
some of mine get really scary lookin, I like em like that now.
If you can, take some pix so we can get an idea of what you want to get rid of.
keep in mind that Stilton cheese is a natural rind and even they don't do anything to prep it, a blue cheese is different, most recipes call for rubbing with salt for a period of time, then they are wrapped in foil and or cheese paper,
there are a lot of videos on the forum on just how Stilton is made, check out some of those threads on the forum and use the search to find some.