You could get a key box like surfers use. It attaches to the car's toeing eye and has a combination lock.
other type are available
I use two solutions - I got a £1 bumbag/fanny pack from Poundland, which I use when I want to take my wallet, keys and phone out running (hey, it's the only time we get to be alone!). If I'm racing or doing a Park Run, I use an old money holder that goes round the waist that I got from Boots. It's really flat although the thinner straps can be uncomfortable.