A more natural English phrase would be They will not want beer, but will want wine. Or they will want wine not beer. For some reason the suggested solution sounds wrong!
Why is 'they won't want beer but wine' wrong?
"They won't want beer but wine" is accepted. But there is a report in the system, from the same time as your comment, for "THE won't want beer but wine." (Oops?)
If that was my mistake, sorry. I'm not sure even if I double checked. Thanks.
That would be very unusual there...