Currently there is no way to move these without using finger / cursor. It isn't a huge issue, but would be nice to have full-site consistency.
There is also the other type with vertical layout and dual-Kanji pairing, but I rarely see them.
This could be done by tagging the hiragana options with 1-6 (focusing it), and then moving the 1-6 keys/display to the Kanji options. After making a selection, the hiragana options would again have the same 1-6 applied, including the already moved one, so it could be moved again.