That sounds perfect. The city also sends out regular patrols, hunting for pirates and raiders and the like, as well as protecting in-coming merchant ships, dignitaries, etc.
Keep in mind that, unlike traditional D&D settings, orcs (well, mechanically half-orcs), gnolls, and several other "evil" races are more civilized and live in the city alongside humans, elves, and dwarves.
That said, dwarves and orcs barely tolerate each other after the orcs withdrew from a nearly 100 year occupation of the dwarven island during which they were less than kind to the dwarven people and their island. The dwarves are trade in gems, precious metals, and stone because the orcs stripped the island of arable soil and killed off most of the food animals on the island.
So, while there is a history of conflict between orcs and dwarves, they are currently at peace. A dwarf character is most likely to be working either for a dwarven merchant or the dwarven ambassador's delegation (this latter option will also provide more story opportunities).