Is there any way to control specific models of printers using Unity app?

I... Personally wouldnt use Unity for something like that, in my opinion, its probably more complicated to use Unity for that, since its naturally a game engine to make visual things happen on a computer, rather then make things happen in real life with the press of a button

I would suggest using something simpler like Visual Studio .NET language, since networking is a little easier, and you can then manually link every printer you want to your application, and chose which one to call a "print" request to, which there are tons of references online on how to set that kind of network application up, and googling something like "vb.net printer commands", "vb.net network or find a printer", "vb.net capture screen shots", youll most likely find good examples or videos or even completed source files/projects you can use.