Here's some specific info on tires for the Ninja -
https://faq.ninja250.org/wiki/Tires
There are choices (unlike what the dealer told you), but they are limited due to the Pregens 16" rims. Later models (2008 and up) have 17s, and a lot more choices.
We have had Pirelli MT75s on one and Diablo Scooters on another Pregen, and they were good, but I have experienced issues with Pirelli's rubber compound (on both cycle and auto tires). The tires tend to be very good initially, but the rubber dries quickly and cracks way before it should.
Dunlop original replacements aren't that great, so I'd consider other options.
Look around, and keep that in-mind, when you are shopping.
Changing tires without the proper equipment can be a real pain. It can be done, but plenty of people try it once before taking them in to a shop. Most reputable shops will spin balance them as well, which is something most DIYers can't do. Tires are not perfect, or the same every time, so they should be balanced when changed.