This is what I did. I also had imminent travel with Hyatt stays. The rep I spoke with said she could approve the card immediately if I moved some credit from another card, which I elected to do. One caveat was because they needed to link my WoH account that I couldn't get expedited shipping on the initial card.

If you have sufficient credit lines on the other cards that you could move to the WoH card, I don't know of a single case of Chase refusing to move credit to get an approval.