Here we present a cost-effective multichannel optomechanical switch and software proportional-integral-derivative (PID) controller system for locking multiple lasers to a single-channel commercial wavemeter. The switch is based on a rotating cylinder that selectively transmits one laser beam at a time to the wavemeter. The wavelength is read by the computer, and an error signal is output to the lasers to correct wavelength drifts every millisecond. We use this system to stabilize 740 nm (subsequently frequency doubled to 370 nm), 399 nm, and 935 nm lasers for trapping and cooling different isotopes of a Yb+ ion. We characterize the frequency stability of the three lasers by using a second, more precise, commercial wavemeter. We also characterize the absolute frequency stability of the 740 nm laser using the fluorescence drift rate of a trapped 174Yb+ ion. For the 740 nm laser we demonstrate an Allan deviation σy of 3×10-10 (at 20 s integration time), equivalent to sub-200 kHz stability.