Hey there,
I feel I should first point out that I am not at all familiar with the anime from which you draw the ideas for your intended Shadowrun campaign. Regardless, there are a few things that I would like to point out:
Firstly, no matter the setting or how cool something is, you should probably initially ask yourself what kind of stuff goes on there so to better pinpoint where from you will draw inspiration to design your adventures.
You mention the Mafia, Triads and a version of the Vory. That, to me, means you have the potential to cover most of the bases from which typical Shadowrun campaigns draw from. Whereas Seattle and Denver-based campaigns often draw the source of Runs from Megacorporations, you can easily swap their role in the scheme of things for that of the three criminal syndicates which are inherent to your chosen source of inspiration.
As for the Runs themselves, well, they can pretty much be anything:
Courier jobs wherein the characters are required to deliver a package (or data, or a person) from one place to another. The place itself can be anything, really: warehouse, camp, house, apartment -- what-have-you. What's more important is the motive behind it: who, in your setting, would want goods moved from place to place and, more importantly, why?
Escort (no, not that kind) duty wherein the characters are hired to serve as a personal security detail for some character or another, possibly in transit from one place to another, or something more localized to a particular venue. Again, so long as you can answer the what, where, why and how of it, it should be no different than if a likewise Run in one of SR's main "hubs".
Infiltration and spy games wherein the characters are hired to operate undercover by one syndicate into the fold of another. It need not be something necessarily done on a very grand scale (especially considering many criminal syndicates operate in several small quasi-independent "cells").
Training wherein the characters are hired to train a certain someone on behalf of their employer (again, drawing from the criminal-element-heavy elements of your intended campaign setting), or, conversely, they themselves must undergo some form of training. The location of your setting can no doubt make for very interesting opportunities for jungle survival, scuba expeditions, exploration, and possibly guerrilla warfare.
Alternatives are nearly limitless in regards to the population at large inhabiting your city: how does the criminal element affect their daily lives? Do they/would they need/want protection? Enough to hire the Runners? Do they also have particular needs that warrant hiring Runners to deal with the syndicates? How about law enforcement? Etc.
Regarding your worry about waterway travel -- there needn't be any. Just make sure to inform your players that, in your setting, the most usual means of transportation is by waterfront and the like. If none of your players pick up a relevant skill in that regard, simply add a boating NPC to the cast of characters who will lessen that difficulty. Of course, you could feasibly run a perfectly fine game in which the characters continuously need to find ways to secure marine transportation so to accomplish their goals.
Allow yourself to be inspired by your chosen setting and take the time to go through the logistics of how the city is run, if for no reason other than to give yourself enough material with which to work. I would recommend you do some quick Wikipedia-ing in regards to the general area wherein your campaign will take place, read up on how the Vory, Triad and Mafia operate. The more information you allow yourself to have access to, the more likely you will be able to come up with solid material to keep a healthy game running.
Good luck and have fun!