SkyClub access connecting from VS UC to DL internal?

Afternoon all,
Wondering if anyone has experience trying to get into a DL SkyClub lounge when they're arriving from a VS Upper Class flight and connecting on to a Delta domestic? I have a choice of connecting on to a flight which has nothing but economy (a little 50-seater), or one which does actually have First. My understanding is that if this was a purely Delta booking, even in First you don't get SkyClub access? This would all be booked under a single PNR with the VS flights, so I guess I'm hopeful that might change it.
I haven't got any status with either airline, or the Platinum Amex.
Thanks!
Wondering if anyone has experience trying to get into a DL SkyClub lounge when they're arriving from a VS Upper Class flight and connecting on to a Delta domestic? I have a choice of connecting on to a flight which has nothing but economy (a little 50-seater), or one which does actually have First. My understanding is that if this was a purely Delta booking, even in First you don't get SkyClub access? This would all be booked under a single PNR with the VS flights, so I guess I'm hopeful that might change it.
I haven't got any status with either airline, or the Platinum Amex.
Thanks!