I have done many 5 day resupplies with sliced dry salami from the deli for during the hottest part of the summer in both the humid east and the dry west. Salamis are loaded with preservatives. Towards the end of the resupply I boil them in my dinner rather than eat them raw. This takes care of live organisms, but it would not take care of their metabolic by-products which can also make you sick. It's unlikely, but not impossible, that you'd have a problem on a 3 day trip with temps @ room temp with sliced salami. You could test this out at home by picking up some dry sliced salami and leaving it on the counter.

In times other than the summer when the weather is cooler, I often take regular sliced deli meats such as turkey or roast beef. I eat them within a few days. Deli cases sometimes have pre-sliced deli meats in small quantities (third-pound) and very convenient sealed packages with an integrated ziplock. The sealed ones will last longer unrefrigerated.

Since I don't do mail-drops, selections are very limited in some of the little trail towns in which you can find yourself trying to fish out a resupply, and finding something like a summer sausage is unlikely. Almost every town has some kind of preserved luncheon meats, though.