Broadly speaking capacitor manufacturing lines don't differentiate between the inner and outer foil leads; they are marked pretty much at random orientation. Even when a band is marked on the cap, you will probably find that it does not indicate the outer foil, but is just "there". Many years ago (and I mean many years ago) the band did mark the outer foil, but it's just there today as some kind of traditional way to mark caps.
If you believe that the manufacturer marks the outer foil, you should confirm that via a query. Most of the time you will learn that the markings are not indicative of orientation, and you will have to measure them with a 'scope.
Create a test lead from Coax and a BNC connector (or whatever is appropriate for your 'scope). Length is not critical but it should be long enough to be able to move it away from equipment that might introduce noise (including the 'scope itself). Perhaps 18 to 24" (400~600mm).
At the BNC end, connect the centre conductor to the Scope positive, and the shield to the Scope Common.
Attach two short leads to the other end of the Coax cable (a few inches/cm, long enough to comfortably reach the leads of the size of caps you want to test, but no longer). Connect the outer (shield) of the Coax to one alligator clip and another clip to the inner conductor of the Coax.
Hook up the two leads of the cap to the two alligator clips, and view the sine wave trace on the 'scope, while holding the body of the cap in your fingers. Then reverse the clips and view the trace again.
The orientation where they Scope trace has the lowest amplitude is the correct orientation (cap outer foil is connected to the shield alligator clip). Mark it somehow (sharpie, tape you remove later if you want a "clean" looking cap in your project, etc)
By holding the cap body in your fingers you are acting as an antenna and inducing the scope trace. The outer foil acts as a shielded element, reducing the induced amplitude.
When installing, the outer foil should be connected to the lower impedance side of the circuit. You may need a schematic to determine that point, while in other cases it will be obvious.
Connecting the caps oriented properly in circuit will reduce the susceptibility of the circuit to induced noise. In the absence of such noise (yeah, right) there should be no difference in measured performance (they are, after all, bipolar caps), but we live in the real world
Also measurable and audible are not always the same thing.
If intended for a passive crossover application, it may not matter much, although in some "capacitor shootouts" it's said it does. In active circuits, that's another matter entirely.
