Incorrect nationality on dCoS

My employer’s lawyer put the wrong nationality on my defined CoS but everything else is correct. He said that i can just mention it in my SWV application and don’t need a sponsor note. I’m meant to start work in 3 weeks and the processing time is within 15 days after my biometrics appointment. I need to submit my application today in order to make it on time. Does anyone have experience with this because i read online that a sponsor note must be included? Any advice would be greatly appreciated, thank you 🙏😭