You can replace the incompatible module with ESP-12 or ESP-07. Besides the module, this process will require a heat gun, soldering tools and moderate soldering skill.

Seems to be identical to LED Starry Sky Projector Light in every way except that the TYWE3S has been replaced with a WB3S.

Transplanting an ESP-12 is confirmed to work using the original template (pinouts are the same), but cheap solder makes it slightly difficult to remove without damaging the contacts.