I think moving/ shaping aura does require manipulation, but it likely doesnt take much skill to get practical use out of it.
So basically i keep seeing people talk about how they dont think you need manipulation to move aura around, but the more i have seen that the more i feel compelled to disagree. To put it in the most basic context i believe that Gyo and Ko inherantly use enhancement, and that your skill in enhancement develops via your use of these techniques even if you never otherwise train in enhancement. I partially beleive this due to the fact that Ko enhances the offensive/defensive power of any nen user who makes use if it, and there really isnt a better explanation for why pure enhancers can do more damage with it then anyone else.
However if we can assume that the use of nen is in many ways grounded in the practical aspects of the various hatsu types it seems to make a great deal of sense reguarding what we consistantly see characters do. Now i can probably get into each nen use from basic to advanced and point out which hatsu seem to affect which aspects, but im pretty sure nobody woyld read that if I did. Instead i want to make a few simple points on the matter, in the hopes of changing peoples minds.
-It is likely shaping/directing aura in simpler ways takes far less specialized training and likely less overall skill to actually achieve. To put it another way it is like the differance between knife throwing and tossing a paper ball in the trashcan, one takes a great deal of practice and training and the other is something that most people can do if somewhat inconsistantly.
-It is likely that in order to form a shape with your aura you require manipulation or conjuration, in the case of manipulation i am implying that forming and potentially holding a shape without that shape being real is what requires manipulation. We see Bisky shaping her aura into numbers when she first trains Gon and Killua, and while im willing to accept that she transmuted her aura into something rigid rnough to hold it's shape that doesnt explain how that shape is formed. Transmuters can force their aura to simulate and alter the nature of real life properties, forces, and substances, there is no substances which naturally want to form into the shape of a number to my knowledge. The only way that makes sense is if she first forms the shape of the aura then transmutes it to hold the shape (same thing with Gon's Janken-scissors btw).
-With reguards to the last point i would like to point out that Bisky likely has around 40% affinity with manipulation, and if the previous point is correct, she only uses it in extremely basic ways overall. While she likely does use some form of manipulation for her hatsu Cookie, its likely that Cookie only works via utilizing preexisting knowledge on related subjects. In other words she is programmed like a machine so she likely cannot be used on nonhumans or really any creature Bisky doesnt have knowledge of reguarding their biology. Much like a CNC machine she cant perform actions she isnt programmed for, but she will absolutely do an amazing job at what she is programmed for. This would also explain why killua jumps over his opponents when he uses his thunderbolt, he not only extends his aura to his target via manipulation he also uses the properties of electricity to do some of the the heavy lifting.
-The last major thing i want to put here is a comparison to Shoot (who i want to beleive is a manipulator or emitter but i really cant find any direct info on that at this point) and what Bisky and Killua can do. Firstly i want to point out that Shoot's bird cage and seperate hands arent specifically anchored to a relative point outside of maybe his body itself. Instead there may or may not be a set limited range, but reguardless he can manipulate the relative position of all three hands and the bird cage in space in real time. Not only is the level of manipulation more complicated then what bisky or killua ever do, he actively can also manipulate multiple objects effectively without their flight paths interrupting eachother. I think the difference in affinity and lack of deicated training in that area can more then account for the limited abilities of nen users who are further from manipulation.
-Small note here about nen beasts with their own personality(this is slightly irrelevent), Kite's crazy slots didnt use much manipulation since he had low affinity with it (probably around 50% affinity if togashi's chart is to be believed). I beleive that his low affinity with manipulation is what results in the clown's "annoying" personality, Kite literally has no control over when it speaks or what it will say even finding his helpful commentary to be annoying and wishing it would shut up. I think that low affinity with manipulation may actually be a condition for autonomously thinking or acting nen beasts.