Here is the X1 Power adapter I've been using for my X1. Works perfectly no issues. Hence you need a Xbox 360 Power supply NOT SLIM or the new ones. Only the Elites and younger.
I run a home business and highly recommend the adapters for the Xbox 360 Slims along with an old 360 phat power brick as the new slim power adapters are garbage..
I'd be more worried about the new power supply than the adapter..