Switch from hardwire to wireless doorbell

We recently decided to change our door chimes from a simple two note bell to a 16 note bell. The instructions said to connect a diode if the whole chime did not play. We installed the diode and it still did not play, so the manufacturer suggested that we need to change the transformer. In searching for the old transformer, it appears the former home owner has sealed it into the basement ceiling when they finished the basement.

Rather than tear one or more holes in the basement ceiling looking for the old transformer (I'm pretty certain it is attached to one of two lighting fixture junction boxes), I'm thinking it might be easier to simply switch to a wireless door bell system. If I try and hook the wireless chime into the power supply coming out of the wall, will their still be a problem since the old transformer is still attached to the power supply to the chime?

The wireless chime is likley going to require regular mains power, or a DC/battery power supply it shouldn't have anything to do with the old chime system at all.

If your wireless chime can safely work from the transformer voltage, you should go ahead and interface it. You can also modify an infant monitor for use in this application.