I use Skyrim Redone (SkyRe) (in German). It recommends running the standalone http://skyrim.nexusmods.com/mods/28467/? in order to ensure that weapons and armors are handled correctly. However, while reading the ReProccer description page I'm getting the impression that it doesn't do anything that Wrye Bash doesn't do.

If I use Wrye Bash in order to create bashed patches which fix/merge leveled lists for weapons and armors, is there any need to use the standalone ReProccer at all?

I've been using the two together with no problems.

Just gotta keep a couple things in mind: first, the reproccer patch comes after the bashed patch. Unchecking the reproccer patch(es) before you make a bashed patch, then reactivating them afterwards is something I tend to do as a way of reminding myself of this, and to avoid Bash accidentally including them in the bashed patch. Second, the bashed patch, in skyrim, is primarily a levelled/form list merger, with a couple tweak options. It's nothing like the Oblivion version, or even the Fallout 3/NV variant. If Bash can make the bashed patch using whatever mods you've got installed, the Reproccer will have no trouble reading the bashed patch when doing its thing.

Reproccer is not for merged leveled list, but for adding SkyRes stats to mod-added weapons and armors. Not the same thing...