A UA/SK codeshare won't make much difference - unlike UA/LH you won't get any Premier bonus miles or anything, so might as well book with SK.

Incidently as a 1K I got a comp'd upgrade out of SK on my last trip (CPH-CDG) and another person I know got a comp on CPH-EWR as a 2P on an award seat (!).

So, definately have that number in there!

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RichardMEL, UA 1K
A Star Alliance Member.