Zuki,
If the arranger is playing, then a LH trigger is fine for simple harmony, but if you require ( desire? ) a more flowing, custom sound, then the right hand is the way to go. Unfortunately, most arrangers link the harmonizer to the auto-chord track, so if you want to stretch your harmony dollar...you also have to modify your playing style.

If you switch the chord recognition to the RH, and play bass, strings or whatever in the left, then you may hear too much movement in the chords from the arranger. Vocalists often use passing tones and "blue" notes to get somewhere....these tones may NOT be quite as subtle coming from a canned arrangement.