You're looking for NorthStar Trekking. They're the vendor for that ship's tour, so there's little issue of reliability... you'll be with the same company either way.
When you call, they MAY tell you to book via your cruise line if they know you're coming on a cruise. Just start off asking for pricing and availability on the date you're here, and see what they say.
There's a chance they'll be "sold out" because the ship has pre-booked all of their tours, or there's a chance the ship will be "sold out" and you can still find a seat or two booking directly. Either way, I would imagine you'll save a few bucks in commissions if you're able to book directly.
Happy Alaska Travels!