To answer your question, we do a number of exercises at our dojo in pairs, but we also have quite a few that can be done alone. We do the bokken happo undo mentioned above, a 4 short "striking" katas where the footwork is basically shihonage, ikkyo, and kokyunage/iriminage (depending on what your school calls it). We also have 3 bokken katas and 3 jo katas, the last of which is done as suwari-waza.
Just a few observations on a letter above:
European styles differ mainly on the weapon used.
for example fencing, depending on foil, sabre, or eepe, is generally very target orientated. you are aiming for specific organs in the body. There is no such crushing blows in fencing, so the strategy basically is to feign the opponent in to moving his defenses out of the small above the waist target area, then strike with a precise killing blow.
Not so, on a couple of counts. I've fenced all 3 weapons, including foil competitively, and I've not known anyone to seek a "precise killing blow."
Perhaps this a weakness of competition, but points (more precisely, "touches" or "cuts") are sought, and anywhere within the alloted area counts the same.
In sabre, the upper half of the body is the target area, and we used a lot of arm and shoulder cuts - could be "killing blow", but not likely.
In epee, the whole body is the target, and since the foot of the opponent is often closest, it was a favorite target, and again hardly a "killing blow" or "organ" being tageted, although I suppose you could bleed to death from a cut foot.
And, lastly, foil. I fenced with, and against, some nationally-ranked coaches and fencers, and never heard of or saw "organ" targeting or much concern for precision targeting as such. In fact, one fencer I knew used ma-ai well to draw in his opponent and then "flicked" his foil downward to the target, holding his wrist in the same place, much like someone casting with a fishing pole. It was very fast, in the target area, but not a killing blow.
SO, I don't mean to be overly critical, but that's my take on it. The feints in fencing can be useful in studying aikido atemi, but except for certain parry/riposte combinations, the foil arts are essentially linear in nature and not circular like aikido. A footnote, fencing derived as an art from ballet(!)