Try hedging this 4 pairs.

buy GBP/JPY 1.1 lot
sell CHF/JPY 1 lot
sell GBP/USD 1.2 lot
sell USD/CHF 1.2 lot

Just like you wanted. You can gain from swap and gain pips from their price differencial if price move in your favor.

or you can use a software to help you calculate lot size allocation for correlation hedge.