The mapping of the detail of paths is something I don't think that OSM has quite got right yet - so some of your issues are to do with this.
That said, I'd encourage you to think about the data first, not the colour that a line appears on any given map. There's a saying in OSM circles which is "don't tag for the renderer". What this means is don't change what you record in the details for a mapped feature because you want something to show up in one particular way on one particular rendering (style of map).
However... on this occasion you're spotting one of the slightly unresolved issues... how to tag to explain that you are allowed to cycle... when you might not actually want to cycle there on an ordinary bike.
You'll be getting blue on the OSM Outdoors rendering because the data says 'bicycle=yes'.
As edd1e_h suggests, it might be better to change this. If you look at nearby paths, even good ones, they record 'mtb=yes'. This has become one way to indicate that you can cycle - but that you might want only to use a mountain bike.
This convention might evolve still further, but it's probably a decent one to use if you want to indicate anything at all about cycling (given that the access legislation implies that you can take an MTB anywhere pretty much).
A good work around at the moment
not resolved
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