You'd have to spend some sort of action (an attack?) to toss the parasol up which seems like it'd reduce the utility of teleporting a bit. Especially if you had to spend another action to draw one from the efficient quiver. Certainly cute though.
Since shadowdancer is a prestige class and as such you should be at least mid-level, just invest in magic items and/or consumables to lower the light level of the area, like scrolls of darkness. Although it may not be cinematically as cool as teleporting between parasols, it will prevent your GM from developing a headache trying to do the physics on how parasols will act in round-by-round combat. How far do they drift? How fast do they fall? How much does wind play a factor? What angle is the sun coming at? Are there torches at ground level? Etc.
Very cool and interesting concept. But for Pathfinder IMHO it's a bit headache inducing and will drag combat out unnecessarily.
From a rules perspective it doesn't really work at all. A parasol doesn't create a lowered illumination area (and if it did, it wouldn't be needed as pretty much anything would be creating such areas.)
I do think it is a cool and flavorful idea. If I was the GM I'd work with you to make something that would work. a 'Darkness parasol' Something priced like a potion of the darkness spell that with a splash object throw to a square roll would make that area reduced light would be one option. A 'quiver' that made X 'darkness parasols' a day would also be workable.
Keep yer vampire umbrellas away from me!
Are you saying that a parasol doesn't cast a shadow?
Not any more (or less) than any other opaque object.
However, despite the name, Shadowjump doesn't need a shadow. It needs an area with dim light. Given that pretty much everything casts a shadow, one must conclude that either a parasol won't work, or is it unnecessary. Only an absolutely featureless plain would really be shadow free.