I would prefer a more generic key or system, to allow one naming system across routes for all transport modes: foot/walking/hiking; bicycle/cycling/mtb; horse riding; motorboat; canoe, and whatever else is or comes around.
There are already too many transport-specific keys as it is, while basically the routes are not that different. From an informational standpoint, that is. They are all strings of ways, grouped together in all kinds of ways.
How about something like operator_network=EuroVelo? That would work across all routes and transport modes, doesn’t repeat information already present (route=bicycle, network=*cn, hence no need to stress again that it’s about cycling).