I think most of the Japanese two handed players seem to gravitate to a saxophone or other woodwind type strap. These usually end in a small snapping hook that will sometimes match the eyelet or otherwise hook onto the hand strap.
As far as hole drilling on most Asian made melodicas there is a plastic shell and then an inner air chamber. it should be fine to drill the outer shell. In fact I usually play with mine off:
HOWEVER! If you are talking about the Hohner Performer 37 the lower part of the shell is the air-chamber so proceed with CAUTION.
On to two-handed playing. Although it has a keyboard (take it from an organist from way back) playing the melodica is nothing like the piano. Your breath is filling the air-chamber, when you press on keys you are opening valves that let the air out and it all comes out evenly so there is no real difference in volume. The lower notes have larger reeds that will vibrate with less pressure so they sound first and louder. Sometimes I’ve even had the low notes rob the air from the melody and it not even sound.
I’ve been noticing some players starting to play two melodicas at once to overcome this. Much as there are two manuals on most organs. https://www.youtube.com/watch?v=EoCnnp2Qx64
I’d reccomend a little table-top playing at first to get an idea what works and doesn’t before trying the left hand over technique.