We now have a wiki!
If you can't use chalk try using a hook grip.Walking should reduce stiffness and soreness do to circulation advancement without developing lactic acid.
You could use a chalk ball in a bag without anyone really noticing. You can buy them from climbing shops, or make one yourself.
From a health and fitness professional perspective (with regard to injury prevention) if you can't lift it with just your grip alone (w/chalk,gloves) you can't lift it.