The development of a superconducting analog to the transistor with extremely low power dissipation will accelerate the proliferation of low-temperature circuitry operating in the milliKelvin regime. The thin-film, magnetically actuated cryotron switch is a candidate building block for more complicated and flexible milliKelvin circuitry. We demonstrate its utility for implementing reconfigurable circuitry by integrating a cryotron switch into flux-summed code-division SQUID multiplexed readout for large arrays of transition-edge-sensor (TES) microcalorimeters. Code-division multiplexing eliminates the noise penalty of time-division multiplexing while being drop-in compatible with the latter's control electronics. However, code-division multiplexing is susceptible to single-point failure mechanisms which can result in an unconstrained demodulation matrix and the loss of information from many sensing elements. In the event of a failure, the integrated cryotron switch provides a zero-signal output from a single TES, enabling the demodulation matrix used to compute TES signals from SQUID signals to be constrained and data recovered from the remaining sensors. This demonstration of configurable error correction provides both a realworld application of the cryotron switch and a foundation for more complex circuitry at milliKelvin temperatures.