Using miles for a CDC on a DL reward flight using VS miles

Am a confused Tonty at the moment.
I've used my miles to get a G to NYC but flying on DL (flight times suited me better) hut I'd also like to use some of my miles to get the CDC which you can do on VS flights but the page on the website says no CDC for code share flights but that is for paid for flights but I've used miles
So does anyone have any experience of using VS miles for a CDC when flying on DL but on a VS reward. The flights are on the DL flight code.
I've used my miles to get a G to NYC but flying on DL (flight times suited me better) hut I'd also like to use some of my miles to get the CDC which you can do on VS flights but the page on the website says no CDC for code share flights but that is for paid for flights but I've used miles
So does anyone have any experience of using VS miles for a CDC when flying on DL but on a VS reward. The flights are on the DL flight code.