My thoughts...
My first one is you need pants (or shorts, if you insist) with pockets and a belt. No offense.
But as far as something on the neck... Why the SwissChamp? Is it becuase you had it around, or do you like the tool combo? It is a good sized SAK, maybe a smaller one like the Huntsman might do the trick, maybe with a small pair of hemostats to replace the very light pliers in the SwissChamp. Combo that with a small capsule, something bigger than a pill vial but maybe not something as pricey as the TAD Life Capsule. (Short cigar tube with a wire-and-tape loop on it?) Sparklite, a couple of tinder tabs, a needle, a couple hooks, a compass and bobbin of specta line or kevlar thread. You carry that WITH a PSK, so if you strip down for some reason you've still got most of you basics covered.
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-IronRaven
When a man dare not speak without malice for fear of giving insult, that is when truth starts to die. Truth is the truest freedom.