I the idea of different scenarios for the immigrants.
There could be a rumor (true or not) that a certain skill is in great demand, or that a fortune can be made dorfs with the right skills. This can be influenced by your broker in trading agreements, as many suggests. So if you specifically request metalsmiths you can get some of those. If you are successful in combat (and especially raiding in the future) you will get more warrior dwarfs looking for employment and looting opportunities. Plus their families and pets.
Some might be more like normal immigrants, looking for a better life. They would be mainly peasants and lowly skilled dwarfs, as I'm assuming most highly skilled workers don't need to seek a better future somewhere else. They would come in fairly small numbers if you fortress have plenty of food and jobs for everyone.
Others could be refugees. These would be more similar to how immigration looks currently. Their skill levels vary wildly, have nothing to do with what you need other than by accident and they can potentially swamp your fortress in huge numbers, if the disaster was nearby. And of course they are wounded and unhappy, maybe even a traveling tantrum spiral. Refusing to help refugees will look very bad to the Mountainhome. On the plus side, they might emigrate after they have been fed, rested and their wounds taken care of.
Others still could be ordered to your fortress by the Mountainhome for some reason. Dunno what reason there could be though, maybe a garrison?
I'd like for them to more like groups than they are today, maybe even named groups like your starting dwarves. They would have an "expedition" leader that would meet with your mayor and you would have some options on what to do with them, like kick them out, welcome them or take care of them until they are ready to leave if they are refugees. Some groups, like mercenaries or the skilled armorsmith you requested, might request offerings to stay. These would become their private property.