USB-C power adapeters are supposed to be more or less interchangeable. Theoretically any USB-C power adapter will work, even with less power. I'm not sure about the quality though of some generic power supply. I would personally insist on a major manufacturer like Lite-On or Flextronics. They're often the OEM's supplier although not all are identified on the power adapter. Or something like Anker or Belkin.
I'm currently using an Apple 30W USB-C power adapter (packaged with a now dead MacBook Air) plus an AmazonBasics USB-C charge cable on a Lenovo where the original 45W power adapter (with captive cable) failed. I think the connector died. But that's the beauty of USB-C. It works fine - most of the time.
The biggest concern would be safety. These can often get really hot and I've heard of the occasional time when a generic power adapter of poor quality caught on fire.