Honestly, even with an 80-20 split, I'd wear whatever I was comfortable running/jumping/boxing in and just go with it on the bike.
Bike shoes are about efficiency on the bike and maybe/arguably comfort during high mileage continuous rides. In this scenario you can loose both (unless that 80% means 80 miles

) and really not notice a difference.
You will 100% notice trying to run or jump or anything else in bike shoes, even those commuter shoes that are made to "walk in".
I agree with Milk, use your patrol shoes, or whatever pair of athletic shoes you have around the house and are comfortable in (like a pair of trail running shoes).