Thank you for your answer! Coincidentally, I will also be flying from KIX back to HNL in F on United. I am a many years 1K and hope that KIX will have a separate facility for F travellers and not have to send us somewhere with all the other *Alliance members with Gold cards.
Apparently ANA has two different sorts of lounges.
The CLUB ANA lounges,
http://www.ana.co.jp/eng/int_svc/lounge/cluban_e.html
and the SIGNET lounges
http://www.anaskyweb.com/us/e/amc/elite/p_3.html
Lounges location inside airport:
http://www.kansai-airport.or.jp/english/map/intgate.htm
Still does not say if CLUB ANA at KIX is only reserved to F class travellers or not. SQ lounges generally offer separate facilities to their F class travellers.