An important challenge for implementing optical signal processing functions such as wavelength conversion or wavelength data exchange (WDE) is to avoid the introduction of linear and nonlinear phase noise in the subsystem. This is particularly important for phase noise sensitive, high-order quadrature-amplitude modulation (QAM) signals. In this paper, we propose and experimentally demonstrate an optical data exchange scheme through cascaded 2nd-order nonlinearities in periodically-poled lithium niobate (PPLN) waveguides using coherent pumping. The proposed coherent pumping scheme enables noise from the coherent pumps to be cancelled out in the swapped data after WDE, even with broad linewidth distributed feedback (DFB) pump lasers. Hence, this scheme allows phase noise tolerant processing functions, enabling the low-cost implementation of WDE for high-order QAM signals. We experimentally demonstrate WDEs between 10-Gbaud 4QAM (4QAM) signal and 12.5-Gbaud 4QAM (16QAM) signal with 3.5-MHz linewidth DFB pump lasers and 50-GHz channel spacing. Error-free operation is observed for the swapped QAM signals with coherent DFB pumping whilst use of free-running DFB pumps leads to visible error floors and unrecoverable phase errors. The phase noise cancellation in the coherent pump scheme is further confirmed by study of the recovered carrier phase of the converted signals. In addition to pump phase noise, the influence of crosstalk caused by the finite extinction ratio in WDE is also experimentally investigated for the swapped QAM signals.