If it were me Id
1) ditch the hand held. They sound awful, pop like mad, look rubbish on camera and are rarely held consistently in the right place to make the audio good.
2) put my g3 on the speaker (inverted to reduce plosives)
3) put the receiver into the mixer to supply Pa
4) take a feed from the mixer for my recording
CARE! personal mics arent always best for PA applications and can be prone to feedback if driven too hard. Mke sure the levels are carefully set up and itll be fine
Peter
Post Production Dubbing Mixer