I would use a couple of Miller dowels (after cramping the joint shut). They are like stepped wooden nails, strong, but wood rather than metal so they don't introduce extraneous stresses. They are held in with glue, and I use Titebond III for these. Yes you will see the dowel ends on the front surface but since dowels are often seen in woodwork, they don't look out of place. Axminster do them, and you'll need a starter kit including the stepped drill. I have used these on dining chairs for a single joint repair.
It won't be as 'proper' as disassembling the chair and regluing, but as said that carries a big risk of damage.