A shaft being "whippy" will be irrelevant on 97% of shots as long as you have your stroke really well worked out. In fact, a whippy shaft will force you to become better, since you must hit with a very pure stroke to avoid unpleasant CB effects. Where it gets dicey is when you have to cue right up against the rail or cueing at a high angle over a ball out in the middle of the table. Even then, you still just have to work a little harder at striking cleanly through the ball and dead along the axis of the shaft. Going with a medium to hard tip can alleviate some of the difficulty but then you'll sacrifice some ability to masse.
Options on non-conical Skinnies:
Players HXT -- shot with one only a few times, can't quite remember what the taper was like but all I remember was it wasn't particularly impressionable one way or another. Good hit I suppose, didn't feel all that different from a traditional shaft if I'm honest. Didn't run any deflection tests.
Pechauer P+ Lite: (only fits Pechauer cues) Good and whippy. A true 11.75mm pro taper. Had a Kamui Black S on it so it got crazy action but obviously as thin shaft with a soft tip it required a really zinging stroke to be able to send the CB 9ft down table when applying maximum draw. Very low deflection. Shaft was way too delicate though and had major ding, dent, and warping issues after only a few months. Maybe I got a dud, maybe they just use poor quality low-density maple.
Lucasi Hybrid Slim: 11.75mm with a 'normal' taper, that is, an old-school taper where the diameter is constant for 7-8 inches and then the taper gently rises. (A true "pro taper" is constant for 10-15 inches). With a skinny shaft like this I don't notice the taper rise, really. A very good solid-hitting shaft, anything but whippy (at least by skinny shaft standards.) The good part about this taper is that it works just as well as a full pro taper in a a closed bridge, but since it tapers up a little sooner than a true pro taper, there's no dramatic taper rise near the joint, so you can REALLY stretch far out across the table with it. I was amazed that it still stroked clean when I was stretched out as far as humanly possible across the table. The shaft is durable and pleasant to play, I've liked how it has held up really nicely.
Katana Bushido: 11.5mm with a LONG pro taper. It rises from 11.5mm to 11.75mm in the first inch of the taper to be a bit stiffer and fit in your bridge better, then that 11.75mm shaft runs back for the next 14 inches so it's very very smooth to stroke. (With the sharp taper rise at the joint though, you'll have to pull out the mechanical bridge rather than just stretch out for certain shots). For such a thin taper, it really has a pretty rigid hit. When you hit this shaft right, you can really juice up a cue ball and keep good control. However, even though I wouldn't describe it as 'whippy', if your stroke is off by even a little bit when you load up with power, you'll get an ugly dead-sounding hit, like the tip is just ringing and bouncing off the CB, almost a semi-miscue. I think it may be in part because the shaft is both fairly rigid for its diameter and incredibly light, weighing only 3.6 ounces with a uni-loc joint. (Other joints may weigh even less). For this reason, I'm actually not digging the Kamui Black M, which is what I prefer on other skinny shafts. I may switch it to a soft or even supersoft (remember the Kamui Blacks hit quite a bit stiffer than other tips, a Black Soft is like a medium, medium+ in other brands.) Still, as long as you hit this shaft pure and do your part, it really performs well. I play snooker with this shaft and honestly it plays better snooker than my snooker cue. I'll have to get a tip just a little bit softer than the Kamui Black M for this shaft for it to hit its full potential playing pool but right now it's amazing on the snooker table.
Seyberts S-tuned Predator Z: 11.85 mm with a long pro taper. Expensive AF. Unfortunately, l I haven't had a chance to shoot with one. I think the Predator Z is a decent shaft and the hit is well balanced, although I'm having a hard time imagining how it would change when you take it down from a conical to a pro taper. Anybody out there have one of these? Seyberts has done this for both the Z2 and Z3 so I'm guessing they have been selling them alright.