According to Tim Krabbé, the record is 17 moves and it's tied between the following games:
Blodig - Wimmer, Germany 1988
1.g3 e5 2.Bg2 d5 3.d3 Nf6 4.Nf3 Nc6 5.O-O h6 6.c3 Be6 7.Nbd2 ...
It seems obvious to me: if it is your move then you MUST touch your own piece first; pick it up with one hand and then pick up the target piece with the same hand and place your capturing piece on the vacated square - although this may require a tiny bit of finger control so be it. The comcept that if you pick up the target piece first, providing options for ...