Please help. My employer applied for a a defined CoS for me but I believe I need an Undefined CoS

[TeaTime]

Dear members, I would be grateful for some help. Thank you.

I am currently in the UK on a graduate route visa that expires on Feb 7th, 2024 and want to switch to the skilled worker visa. I have been offered a job that can start anywhere from Feb 7th to March 27, 2024. My employer put in an application for a defined CoS for me, but I believe I need an undefined CoS since I am in the country and already on a visa. Should I ask them to withdraw the Defined CoS application and reapply for an undefined CoS? I have not started my application, and am waiting on the CoS. My employer's application for the defined CoS just went it and it hasn't yet been assigned to me yet. I, obviously, need to apply for my visa before Feb 7th, so just wanted to make sure everything is in order. I will do the expedited service.

Thank you. I would be grateful for advice.

[AmazonianX]

As you are in country and to make an in country application the UCoS as you have identified is appropriate.

Worst case CoS is not assigned before your visa expiration then you will have to exit UK to home country to make the application thereby making the DCoS most appropriate.
As CoS assignment taking time now, asking for cancellation of the in progress DCoS dicey.