There might be another reason to not soak it. It looks like the head
is quite old. There may be some stress cracks that you can't see.
Soaking the handle after a snug fitting will cause the wood to expand,
indeed, it may expand so much that it breaks the head. The power of
expanding wet wood is well illustrated by the old technique of
quarrying stone with wooden wedges. The quarrymen would chisel holes
along the line of desired breaking, pound in dry wooden wedges, then
soak the wedges in place. The swelling wood would put so much
pressure on the rock it would split it right off.

Also, when wetted and confined, wood can expand so much that the
fibers are crushed, and when the wood dries out again it is looser
than when it started. This is one of the primary reason that wood
joints fail over time in climates that have large seasonal humidity
changes.