I think you're over doing things. First, at a remake just use the same trap no problems. On a trap that has caught and you are moving it to a new location wash off the mud, blood etc and usually you can put it back in the ground...yes there will be some rust in the exposed areas but this shouldn't be a mjor factor. If you want to go a step further, after you rinse off the crud, soak the trap in some hot water with a cap of bleach. After a few mins. soak, rinse in hot water and hang to dry...the trap is now decontaminated.
Look, if you have an aboundance of traps or time, it is always more comforting to start each set with a freshly preped trap. However, this is the real world and all that fuss isn't an absolute.