OSM mapping: sett or cobbleston

Dear all, I use to change OSM data, because I found some roads are not mapped correctly in my area. I found here (https://cycle.travel/about/maps) that the surfacetag "cobblestone" is used to qualify a road. OSM recommends to use a more precise value such as "sett" or "unhewn_cobblestone". So, because it is recommended by OSM I used "sett" and added the smothness tag.

Is it possible to add "sett" to the used values to determine the surface, should I add cobblestone also to the tags in OSM, or is there an other way to satisfy both, OSM and cycle.travel?

Tanks in advance!