Yup, likely both is a good solution. Add CMC (say 1-10mH), add Y cap from mains-N (either side of the CMC -- try both ways, see which works better) to secondary side, GND or whatever it is.
Sometimes helps to use a small CMC on the secondary side, alone or in combination with the primary side choke. How useful this is, really depends on where the noise is, if it's truly common mode between primary and secondary, or if there's some to ground or free space or something like that. Whether the module is bare PCB or enclosed metal, etc.
Don't forget to re-check the original one in the same ways; it could always be that the new one has exacerbated emissions from the first.
Tim