additional minimal size kit you might consider

an N95 mask should offer some protection against airborne alpha emitting particulate...you really don't want alpha emitters inside you...bandana

an MRE beverage bag and some ClO2 tabs easily fit in the pocket...possibly dumpster dive for a bottle, and use a provodine wipe to disinfect externally and internally

small card of duct tape to pre tape potential hot spots on your feet if a long trek is in store...stash a pair of wool socks

a small multitool like Leatherman squirt PS4 has small pliers, scissors, knife, screwdriver and is 3/4 x 2 1/4...