Shamans have perks, but in general any ranged DPS is much easier to handle than melee. It's not something you can really ever "solve," but you can work with it if you want to do so.

PVP is where multiple-melee tends to be completely useless, and where shamans tend to be strongest (tremor totem rotations). For only-PVE multiboxing, you can be much more flexible. Any ranged DPS class will work well, melee DPS will work with great effort, although some options won't have the stacking benefits shamans do like more totems, off-healers, wipe recovery, etc.