Two thoughts:
1) not sure what aspects of the cord bothers you, if it is because it is simply "in the way" you could drive the PC88 into a tiny
mixer positioned behind you, then connect your headphones to the tiny mixer. this would alleviate the cord from being "in the way".
2) purchase a 1/4" to 1/8" converter
(link) which you would plug the 1/4" end into the PC88. Purchase a Blue tooth transmitter
(link2) which you would plug into the the 1/8" female end of the converter.
My only caution would be latency; link2 above is an example of a blue tooth transmitter. Depending on the quality there could be unacceptable latency (aka delay) between striking the keys and hearing the sound transmitted to the bluetooth pods. I tried this as an experiment with a stereo unit using the headphone jack of the audio receiver as the source, to a bluetooth speaker about 15 feet away. I also had the audio receiver's speakers on. The audio on the bluetooth severely trailed the audio coming out of the main speakers, like a giant echo chamber. guitar wireless systems are known to have as little as 6ms of latency, of course they cost much more as well and they are not stereo. So there will be tradeoffs.
Bluetooth 5.0 and AptX are supposedly designed for lower latency. Is it acceptable? Hard to say without trying it yourself. Ensure your vendor has a good 'return' policy in the event you find the latency unacceptable.