At my table I would rule that they don’t stack. Adding you WIS to your Arcana skill feels like a yes/no trigger. Either you ad it or you don’t, but you don’t add it twice.
Someone brought up the Paladin aura as an example, but that’s not equivalent. The Paladin aura allows players to add the Paladin’s CHA as a bonus to their saving throws, not add their own CHA to their existing Charisma saving throw (although I suppose the Paladin adds their own CHA to their existing Charisma save). Furthermore, it explicitly says 2 Paladins’ auras don’t stack, which would be a closer example (although admittedly not the same).