Second foam and papermache. Give yourself at least 10 day to papermache after you carved it. (One layer a day and letting it dry for 20 hour before starting the next)
I would normally work with insulation sheet foam but because of the structure of the sword making a armature first then covering in foam sounds like a good idea.
If you have any large air pockets you can fill them in with more expanding foam.
As for the paste I use wood glue at 50:50 ratio of water. Unlike White glue Wood glue is sand-able.
My scythe from last year is only reinforced with papermache and a PVC pipe at the bottom if the head/neck.
I got away with 8 layers but 10 layer is more ideal with a thinner structure.